Marco Vianello: scientific and didactic curriculum

Short CV

• Born in Venice on October 26, 1961
  
  
• Married with Giulia, father of Marianna (1995) and Elisa (2000)
  
  
• Laurea (first degree) in Mathematics, July 03, 1987 at the University of Padova
  
  
• Ph.D. in Computational Mathematics, June 24, 1992 (italian north-eastern universities consortium: Bologna-Padova-Trieste-Udine)
  with the thesis Extensions and numerical applications of the Liouville-Green approximation, advisor Prof. R. Spigler, referee Prof. F.W.J. Olver (College Park)
  
  
• INdAM Research Fellowship (Nov. 1991 - Aug. 1992, Nov. 1992 - Oct. 1993)
  
  
• Ricercatore (Lecturer) of Numerical Analysis at the Faculty of Science of the University of Padova (December 1993 - September 2000)
  
  
• Associate Professor of Numerical Analysis at the Dept. of Mathematics of the University of Padova (October 2000 - April 2017)
  
  
• National Scientific Qualification (Abilitazione Scientifica Nazionale) as full professor of Numerical Analysis, December 2013
  
  
• Full Professor of Numerical Analysis at the Dept. of Mathematics of the University of Padova (May 2017-)
  
  

Research results

• over 160 mathematical papers in the fields of:
  Multivariate Approximation Theory - Numerical Quadrature and Cubature
  Numerical Methods for Differential and Integral Equations - Asymptotic Approximations
  with 39 co-authors (13 international), published in 63 journals/books
  
  • over 1100 citations by over 600 authors on MathSciNet
    
  • over 3400 citations on Google Scholar
    
• several numerical software packages

The paper "Quadrature Based Polynomial Optimization'', Optim. Lett. 14 (2020), written with A. Martinez, F. Piazzon and A. Sommariva
has been selected as co-winner of the OPTL Best Paper Awards for 2020

research fields

• Multivariate Approximation: Polynomial and Meshless Approximation, Numerical Cubature (109 papers)
  
  
• Asymptotics/numerics: Differential and Difference Eqs., Fast Summation, Special Functions (28 papers)
  
  
• Constructive/numerical Methods for Integral Equations and Transforms (10 papers)
  
  
• Approximation of Matrix Exponentials and Exponential Integrators for ODEs/PDEs (8 papers)
  
  
• Numerical Functional Analysis (8 papers)
  
  

relevant topics in multivariate approximation (with intersections):

• Multivariate Interpolation and Regression
  
  
• Quadrature, Cubature and Summation
  
  
• Polynomial Inequalities and Norming Meshes
  
  
• Interpolation and Integration Methods for PDEs
  
  
• Polynomial Optimization via Approximation Theory
  
  
• Meshless Approximation
  
  

Special Point Sets for Interpolation, Regression, Integration, Optimization and Collocation

• Padua Points
  Bivariate polynomial interpolation on the square at new nodal sets
  with M. Caliari and S. De Marchi, Appl. Math. Comput. 165/2 (2005), 261--274
  Padua interpolation points appeared here for the first time
  
  
• Approximate Fekete Points
  Computing approximate Fekete points by QR factorizations of Vandermonde matrices
  with A. Sommariva, Comput. Math. Appl. 57 (2009), 1324--1336
  the QR algorithm for approximate Fekete points appeared here for the first time
  
  
• Subperiodic Trigonometric Points
  Subperiodic trigonometric interpolation and quadrature
  with L. Bos, Appl. Math. Comput. 218 (2012), 10630--10638
  the main ideas of subperiodic harmonic approximation appeared here for the first time
  
  
• CATCH (Caratheodory-Tchakaloff) Points
  Compression of multivariate discrete measures and applications
  with A. Sommariva, Numer. Funct. Anal. Optim. 36 (2015), 1198--1223
  NNLS for multivariate Tchakaloff quadrature points appeared here for the first time
  
  
• Polynomial Optimization by Algebraic Quadrature Points
  Quadrature-based polynomial optimization
  with A. Martinez, F. Piazzon and A. Sommariva, Optim. Lett. 14 (2020), 1027--1036
  the first connection of polynomial optimization theory with quadrature theory
  co-winner of the OPTL Best Paper Awards for 2020
  
  
• TDW (Tchakaloff-Davis-Wilhelmsen) Points
  Computing Tchakaloff-like cubature rules on spline curvilinear polygons
  with A. Sommariva, Dolomites Res. Notes Approx. DRNA 14 (2021), 1--11
  the first application of Davis-Wilhelmsen theorem on Tchakaloff sets (1967-1976) via NNLS
  
  
• Unisolvence of Random Unsymmetric Kansa Collocation
  Nonsingularity of unsymmetric Kansa matrices: random collocation by MultiQuadrics and Inverse MultiQuadrics
  with R. Cavoretto, A. De Rossi, F. Dell'Accio and A. Sommariva, preprint (2024)
  the first proof of unisolvence of unsymmetric MQ Kansa collocation for PDEs
  
  

selected codes

• Adaptive bivariate Chebyshev approximation, Numer. Algorithms 38 (2005)
  (with A. Sommariva, R. Zanovello)
  this algorithm is quoted in the 2D freeform surface generator of the ZEMAX OpticStudio package
  see the paper Design & Implementation of a New Freeform Surface Based on Chebyshev Polynomials
  
  
• Product Gauss cubature over polygons based on Green's integration formula, BIT Numerical Mathematics 47 (2007)
  (with A. Sommariva)
  this algorithm has been cited/used in many works on numerical PDEs, see its GoogleScholar page
  
  
• Algorithm 886: Padua2D -- Lagrange Interpolation at Padua Points on Bivariate Domains, ACM TOMS 35-3 (2008)
  (with M. Caliari, S. De Marchi) published in the Netlib
  a variant of this algorithm has been used in the subroutine Fun2D of the CP2K simulation package for molecular dynamics
  by M. Guidon, J. Hutter and J. VandeVondele
  (see Robust Periodic HartreeFock Exchange for Large-Scale Simulations Using Gaussian Basis Sets, J. Chem. Theory Comput. 5, 2009)
  
  
• Gauss-Green cubature and moment computation over arbitrary geometries, J. Comput. Appl. Math. 231 (2009)
  (with A. Sommariva)
  also this algorithm has been cited/used in many works on numerical PDEs, see its GoogleScholar page
  in particular the Matlab code has been used in the CFD package
  SADoRe: Highly Accurate Lagrangian Flux Calculation via Algebraic Quadratures on Spline-Approximated Donating Regions
  by Q. Zhang (see On Donating Regions: Lagrangian Flux through a Fixed Curve, SIAM Review 55, 2013)
  
  
• Computing approximate Fekete points by QR factorizations of Vandermonde matrices, Comput. Math. Appl. 57 (2009)
  (with A. Sommariva); Matlab package WAM
  a variant of this algorithm has been used in state of the art Digital Filters Design
  A Robust and Scalable Implementation of the Parks-McClellan Algorithm for Designing FIR Filters
  by F.-I. Filip, ACM Trans. Math. Software 43 (2016)
  
  
• Padua2DM: fast interpolation and cubature at the Padua points in Matlab/Octave, Numer. Algorithms 56 (2011)
  (with M. Caliari, S. De Marchi, A. Sommariva) published in the Netlib
  interpolation at the Padua points has been inserted in the Chebfun package
  see N. Hale and A. Townsend, Padua points in Chebfun2, Chebfun site, July 2014
  
  
• Compression of multivariate discrete measures and applications, Numer. Funct. Anal. Optim. 36 (2015)
  (with A. Sommariva); Matlab code comprexcub.m
  a variant of this algorithm has been used within the parallel multiphysics finite-element research code BACI
  developed at the Institute for Computational Mechanics, TUM Muenchen (cf. paper 112 in the list below)
  
  
• CaTchDes (Matlab codes for Caratheodory-Tchakaloff Near-Optimal Regression Designs - v1.0 - SoftwareX 10 2019)
  (with L. Bos)
  
  
• Evaluating Lebesgue constants by Chebyshev polynomial meshes on cube, simplex and ball
  (with L. Bialas-Ciez, D. Kenne, A. Sommariva); Matlab codes in dimension 2 and 3 LEBEVAL
  
  

Research collaboration and coordination experience

• Co-founder of the CAA: Padova-Verona Research Group on Constructive Approximation and Applications
  
  
• Member of the national research network: RITA (Rete ITaliana di Approssimazione)
  
  
• Member of the national SIMAI ANA&A Activity Group
  
  
• International collaborations (visits, co-authorship, research projects, ...) with
  
  • Brian Bauman (Lawrence Livermore National Laboratory, USA)
    
  • Leokadia Bialas-Ciez (Jagellonian University, Krakow)
    
  • Len Bos (Univ. of Calgary until 2009, Univ. of Verona 2009 - present)
    
  • Jean-Paul Calvi (Univ. Toulouse III)
    
  • Mahadevan Ganesh (Colorado School of Mines, Golden)
    
  • Dimitri Jordan Kenne (Jagellonian University, Krakow)
    
  • Paul Leopardi (ANU ACCESS-NRI, Canberra)
    
  • Norm Levenberg (Indiana University, Bloomington)
    
  • Maryam Mohammadi (Kharazmi University, Tehran)
    
  • Francesca Rapetti (Univ. Cote d'Azur, Nice)
    
  • Najoua Siar (Univ. Ibn Tofail, Kenitra-Morocco)
    
  • Wolfgang A. Wall (TUM, Muenchen)
    
  • Yuan Xu (Univ. of Oregon, Eugene)
    
  • Sudhakar Yogaraj (Indian Inst. of Technology, Goa)
    
  • Shayne Waldron (University of Auckland)
    
    
• Co-autorship with 36 researchers
  
  
• Advisor of 3 Ph.D.s at the Doctoral School in Mathematics (Curriculum in Computational Mathematics) of the University of Padova:
  Alvise Sommariva 1999, Marco Caliari 2002, Federico Piazzon 2016, see also The Mathematics Genealogy Project
  
  
• Supervisor of 4 Postdocs at the Dept. of Mathematics of the University of Padova:
  Alvise Sommariva 2000-2004 (presently associate professor at the University of Padova)
  Angeles Martinez 2005-2006 (presently associate professor at the University of Trieste)
  Marco Caliari 2006-2007 (presently full professor at the University of Verona)
  Federico Piazzon 2017-2019 (presently tenure-track professor at the University of Padova)
  
  
• Supervisor of 10 master theses for the degrees in Mathematics that have led to 19 scientific publications in collaboration with the students
  
  
• Coordinator of 20 local annual projects on topics of multivariate approximation and applications (years 2005-2024, about 3 kEuros and 3 researchers per year)
  
  
• Coordinator of a Padova University project on "Efficient approximation methods for nonlocal discrete transforms" (2003-2004, 35 kEuros, 8 researchers)
  
  
• Local coordinator of a PRIN 2003 national project on "Approximation of matrix functions in the numerical solution of differential equations"
  (2004-2005, national coordinator L. Lopez, Bari; peer-review score 90/100, 28 kEuros, 4 researchers)
  
  
• Local coordinator of a PRIN 2009 national project on "Locating near-optimal nodal sets for multivariate interpolation"
  (national coordinator L. Bos, Verona; peer-review score 95/100, not funded)
  
  
• National coordinator of a PRIN 2011 national project on "Multivariate Interpolation by Polynomials, RBF and other Bases and Applications"
  (pre-selection peer-review score 98/100, not funded in the national selection)
  
  
• Coordinator of a INdAM-GNCS annual project on "Multivariate approximation by polynomial and radial bases" (2012, 5 kEuros, 5 researchers)
  
  
• Coordinator of a Padova University project on "Numerical Modelling by Tchakaloff-like Cubature" (2020-21, peer-review score 92.4/100, 14 kEuros, 6 researchers)
  
  
• Global research funding as a coordinator 2003-2023: about 143 kEuros with 5 average researchers per year (about 1.3 kEuros/researcher/year)
  
  
• Scientific responsible of a Poatdoc fellowship project on "Numerical Modelling by Caratheodory-Tchakaloff Quadrature Compression"
  at the Dept. of Mathematics of the University of Padova (2019, peer-review score 97/100)
  
  
• Member of the Scientific board (Commissione Scientifica) for research in Mathematics and Computer Science, University of Padova (2004-2005)
  
  
• Member of the Board of the Doctoral School in Mathematics (Curriculum in Computational Mathematics) of the University of Padova (2005-2010)
  
  
• Member of the Board of the Doctoral School in Mathematics of the University of Padova (2019-2020)
  
  

Conference organization and editorial experience

• Member of the organizing and scientific committees of
  1st Dolomites Workshop on Constructive Approximation and Applications (DWCAA06), Alba di Canazei (Trento, Italy), Sept. 8-12 2006
  2nd Dolomites Workshop on Constructive Approximation and Applications (DWCAA09), Alba di Canazei (Trento, Italy), Sept. 4-9 2009
  3rd Dolomites Workshop on Constructive Approximation and Applications (DWCAA12), Alba di Canazei (Trento, Italy), Sept. 9-14 2012
  4th Dolomites Workshop on Constructive Approximation and Applications (DWCAA16), Alba di Canazei (Trento, Italy), Sept. 8-13 2016
  
  
• Member of the scientific committees of
  New Trends in Numerical Analysis - Theory, Methods, Algorithms and Applications (NETNA2015), Falerna (CZ), Italy, June 18-21 2015
  5th Dolomites Workshop on Constructive Approximation and Applications (DWCAA20), Alba di Canazei (Trento, Italy), postponed to Sept. 2021
  Approximation: Theory, Methods and Applications ATMA2023 , Padova (Italy), January 18--20 2023
  Software for Approximation SA2023 , Torino (Italy), February 8-10 2023
  6th Dolomites Workshop on Constructive Approximation and Applications (DWCAA24) , Alba di Canazei (Italy), Sept. 9-13 2024
  Software for Approximation SA2025 , Torino (Italy), February 5-7 2025
  
  
• Member of the organizing committees of
  Dolomites Research Week on Approximation 2007 (DRWA07), Alba di Canazei (Trento, Italy), Sept. 3-7 2007
  Dolomites Research Week on Approximation 2008 (DRWA08), Alba di Canazei (Trento, Italy), Sept. 8-11 2008
  Dolomites Research Week on Approximation 2010 (DRWA10), Alba di Canazei (Trento, Italy), Sept. 6-10 2010
  Dolomites Research Week on Approximation 2011 (DRWA11), Alba di Canazei (Trento, Italy), Sept. 5-9 2011
  Dolomites Research Week on Approximation 2013 (DRWA13), Alba di Canazei (Trento, Italy), Sept. 9-13 2013
  Workshop on Multivariate Approximation celebrating Prof. Len Bos 60th birthday, Verona (Italy), Nov. 29-30 2013
  Dolomites Research Week on Approximation 2014 (DRWA14), Alba di Canazei (Trento, Italy), Sept. 8-12 2014
  Dolomites Research Week on Approximation 2015 (DRWA15), Alba di Canazei (Trento, Italy), Sept. 5-8 2015
  Dolomites Research Week on Approximation 2017 (DRWA17), Alba di Canazei (Trento, Italy), Sept. 4-8 2017
  Approssimazione Multivariata: Teoria ed Applicazioni (AMTA 2017), Palermo, Italy, Dec. 8-10 2017
  Dolomites Research Week on Approximation 2018 (DRWA18), Alba di Canazei (Trento, Italy), Sept. 10-14 2018
  
  
• Co-Managing Editor (2008-2022) and Editor (2023-2024) of the Diamond Open Access journal Dolomites Research Notes on Approximation
  formerly published by the University of Verona and presently by Padova University Press
  indexed in DOAJ // EMIS // MathSciNet // Scopus // ISI-WoS // Zentralblatt
  Q2 Scimago Journal Ranking 2017-2024
  
  
• Co-Editor-in-Chief (2024-) of Journal of Approximation Software (JAS) , Diamond Open Access - Univ. of Torino SIRIO@UniTO
  
  
• Guest Editor of the Proceedings of DWCAA06, special issue of Numerical Algorithms
  
  
• Guest Editor of the Proceedings of DWCAA09, special issues of Numerical Algorithms and Calcolo
  
  
• Guest Editor of the Proceedings of the Workshop on Multivariate Approximation celebrating Prof. Len Bos 60th birthday (Verona, November 2013),
  special issue of Dolomites Research Notes on Approximation
  
  
• Guest Editor of the Proceedings of DWCAA16, special issue of Dolomites Research Notes on Approximation
  
  

Research evaluation experience

• Member of the evaluation board of doctoral dissertations for the Doctoral School of Science and High Technology of the University of Turin (2010)
  
  
• Member of the Committees for the selection of Postdoc fellowship projects at the Dept. of Mathematics of the University of Padova (2012, 2017, 2018, 2024)
  
  
• Referee for the INdAM Fellowships in Mathematics for Experienced Researchers cofunded by Marie Curie Actions (2012)
  
  
• Referee for the European Commission FP7 program concerning Marie Curie individual fellowship proposals (2012)
  
  
• Member of the Graduate Admission Commitee for the Doctoral School in Mathematics (Curriculum in Computational Mathematics) of the University of Padova (2013)
  
  
• Project reviewer for the FWO Research Foundation of Flanders, Belgium (2013-2015)
  
  
• Selected by the FWO board for the triennial expert panel W&T5: Informatics and Knowledge Technology (January 2016; declined for personal reasons)
  
  
• Reviewer of a book proposal (area: applied and computational mathematics) for the publisher CRC Press - Taylor & Francis Group (2016)
  
  
• Referee for the volume "Contemporary Computational Mathematics - a celebration of the 80th birthday of Ian Sloan", J. Dick, F. Kuo, H. Wozniakowski Eds., Springer (2017)
  
  
• Project reviewer for the National Research, Development and Innovation Office of Hungary, Panel "Mathematics and Computer Science" (2018)
  
  
• Project reviewer for the FWF Austrian Science Fund (2018)
  
  
• Project reviewer for the NCN National Science Center of Poland (2020)
  
  
• Research products reviewer for the ANVUR Italian National Agency (2022)
  
  
• Member of the National Scientific Habilitation Committee to associate and full professorships in Numerical Analysis (2024-26)
  
  
• Member of the Committee for a tenure-track position in Numerical Analysis at the Dept. of Mathematics of the University of Padova (2024)
  
  
• Referee selected by over 50 international journals:
  * Advances in Applied Mathematics * Advances in Computational Mathematics * Advances in Difference Equations * AIMS Mathematics
  * Annales Polonici Mathematici * Applied and Computational Mathematics * Applied Mathematics and Computation
  * Applied Mathematics Letters * Applied Numerical Mathematics * BIT Numer. Math. * Bollettino dell'Unione Matematica Italiana
  * Bulletin des Sciences Mathematiques * Calcolo * Computers and Mathematics with Applications * Constructive Approximation
  * Dolomites Research Notes on Approximation * Electronic Transactions on Numerical Analysis * Engineering Analysis with Boundary Elements
  * European Journal of Mechanics * Experimental Mathematics * Foundations of Computational Mathematics
  * IEEE Transactions on Signal Processing * IET Image Processing * IMA Journal of Numerical Analysis * Indagationes Mathematicae
  * International Journal of Computer Mathematics * International Journal for Numerical Methods in Biomedical Engineering
  * International Journal for Numerical Methods in Engineering * Journal of Approximation Software * Journal of Approximation Theory
  * Journal of Computational and Applied Mathematics * Journal of Computational Physics * Journal of Foundations of Computational Mathematics
  * Journal of Inequalities and Special Functions * Journal of Mathematical and Fundamental Sciences
  * Journal of Scientific Computing * Mathematical Methods in the Applied Sciences * Mathematical Programming
  * Mathematics and Computers in Simulation * Mathematics of Operations Research * Mediterranean Journal of Mathematics
  * Numerical Algorithms * Numerical Mathematics: Theory, Methods and Applications * Numerische Mathematik
  * Optimization Methods and Software * Proceedings of the AMS * Proceedings of the Royal Society A
  * Rendiconti dell'Istituto di Matematica dell'Università di Trieste * Rendiconti di Matematica e delle sue Applicazioni
  * SIAM Journal on Numerical Analysis * SIAM Journal on Scientific Computing * Statistics and Computing * Vietnam Journal of Mathematics
  
  

5 selected presentations at international conferences

• "A vector-valued version of Peano's Kernel Theorem"
  3rd Intern. Conf. on Functional Anal. and Approx. Theory (FAAT 1996), Maratea (Italy) Sept. 1996
  
  
• "Near-optimal interpolation and quadrature in two variables: the Padua points"
  5th European Congress of Mathematics (5ECM), Amsterdam July 2008
  
  
• "New Tools for Multivariate Polynomial Approximation"
  ICIAM 2011, Vancouver (Canada) July 2011
  
  
• "Polynomial Meshes and Discrete Extremal Sets"
  3rd Dolomites Workshop on Constr. Approx. and Applic. (DWCAA12), Canazei (Italy) Sept. 2012
  
  
• "Quadrature of Quadratures: Compressed Sampling by Caratheodory-Tchakaloff Points"
  2nd Joint Meeting Spain-Brazil in Mathematics, Cadiz (Spain) Dec. 2018
  
  

selected citations

• 6, 24, 29 in: NIST Handbook and Digital Library of Math. Functions, Chapter 2: Asymptotic Approximations (F.W.J. Olver and R. Wong), 2.9: Difference Equations
  
  
• 11, 17 in: E. Kartsatos (Ed.), Theory and Applications of Nonlinear Operators of Accretive and Monotone Type, Marcel Dekker, New York, 1996 (Ch. 6)
  
  
• 25, 36 in: V. Berinde, Iterative Approximation of Fixed Points, Springer, 2007
  
  
• 26, 33 in: G. Mastroianni and G. Milovanovic, Interpolation processes: Basic theory and applications, Springer Monographs in Mathematics, 2008
  
  
• 43 in: C. Lubich, From Quantum to Classical Molecular Dynamics: Reduced Models and Numerical Analysis, EMS Press, 2008
  
  
• 20 in: C. Kuhen, Multiple Time Scale Dynamics, Springer Applied Mathematical Sciences 191, 2014
  
  
• 69, 80, 84, 85 in: G. Fasshauer and M. McCourt, Kernel-based Approximation Methods using MATLAB, World Scientific, 2015
  
  
• 4, 6, 14, 20, 29, 49, 58, 64 in: S. Bodine and D.A. Lutz, Asymptotic Integration of Differential and Difference Equations, Springer LNM 2129, 2015
  
  
• 61 in: A. Cangiani & al., hp-Version Discontinuous Galerkin Methods on Polygonal and Polyhedral Meshes, SpringerBriefs in Mathematics, 2017
  
  
• 90, 95 in: W. Gautschi, A Software Repository for Orthogonal Polynomials, SIAM e-books, 2018
  
  
• 57 in: G. Plonka & al., Numerical Fourier Analysis, Chapter 8 - High-Dimensional FFT, Birkhauser, 2018
  
  
• 90, 95 in: W. Gautschi, A Software Repository for Gaussian Quadratures and Christoffel Functions, SIAM e-books, 2020
  
  
• 61, 74 in: M. Cicuttin, A. Ern and N. Pignet, Hybrid high-order methods. A primer with application to solid mechanics , Springer, 2021 (arXiv preprint 2106.09348)
  
  
• 79, 85 in: B. Adcock, S. Brugiapaglia, and C. G. Webster, Sparse Polynomial Approximation of High-Dimensional Functions , SIAM, 2022
  
  
• 61, 74, 104, 132 in: The Virtual Element Method and its Applications , P.F. Antonietti, L. Beirao da Veiga, G. Manzini, Eds., SEMA SIMAI Springer Series, vol. 31, 2022
  Chapter 4, E. Artioli, S. de Miranda, L. Patruno and M. Visinoni, Some Virtual Element Methods for Infinitesimal Elasticity Problems, pp. 137--183
  
  

• 57 in: N. Levenberg, Approximation in C^n, Surveys in Approximation Theory 2 (2006)
  
  
• 21 in: P. Butzer and L. Volkmann, Otto Blumenthal (1876-1944) in retrospect, J. Approx. Theory 138 (2006)
  
  
• 34, 43, 45, 46, 52 in: M. Hochbruck and A. Ostermann, Exponential Integrators, Acta Numerica 19 (2010)
  
  
• 48, 57, 62, 69, 71 in: T. Bloom, L. Bos, J.-P. Calvi and N. Levenberg, Polynomial Interpolation and Approximation in C^d, Ann. Polon. Math. 106 (2012)
  
  
• 74 in: Q. Zhang, On donating regions: Lagrangian flux through a fixed curve, SIAM Rev. 55 (2013)
  
  
• 48 in: N. Hale and A. Townsend, Padua points in Chebfun 2, Chebfun Examples - Approximation (2D) - (2014)
  
  
• 71, 75, 85 in: S.-I. Filip, A Robust and Scalable Implementation of the Parks-McClellan Algorithm for Designing FIR Filters, ACM Trans. Math. Software 43 (2016)
  
  
• 57, 107 in: L.N. Trefethen, Cubature, approximation, and isotropy in the hypercube, SIAM Rev. 59 (2017)
  
  
• 126, 136 in: E. de Klerk and M. Laurent, A survey of semidefinite programming approaches to the generalized problem of moments and their error analysis,
  Chapter in: World Women in Mathematics 2018, Springer, 2019
  
  
• 79, 85 in: L. Guo, A. Narayan and T. Zhou, Constructing Least-Squares Polynomial Approximations, SIAM Rev. 62 (2020)
  
  

Complete list of mathematical publications

Preprints

1. Unisolvence of Kansa collocation for elliptic equations by polyharmonic splines with random fictitious centers, arXiv: 2410.03279 (with M. Mohammadi and A. Sommariva).
   
   
2. Unisolvence of unsymmetric random Kansa collocation by Gaussians and other analytic RBF vanishing at infinity, arXiv: 2405.18550 (with A. Sommariva).
   
   

   2025

3. Nonsingularity of unsymmetric Kansa matrices: random collocation by MultiQuadrics and Inverse MultiQuadrics, arXiv: 2403.18017, Math Comput. Simul., minor revision (with R. Cavoretto, A. De Rossi, F. Dell'Accio and A. Sommariva).
   
   
4. Random sampling and polynomial-free interpolation by Generalized MultiQuadrics, J. Approx. Theory 306 (2025), 106119 (with A. Sommariva).
   
   

   2024

5. CPOLYMESH: Matlab and Python codes for complex polynomial approximation by Chebyshev admissible meshes, JAS - J. Approx. Software 1, 2 (2024) (with D. Kenne and A. Sommariva).
   
   
6. Evaluating Lebesgue constants by Chebyshev polynomial meshes on cube, simplex and ball, Electron. Trans. Numer. Anal. 60 (2024), 428--445 (with L. Bialas-Ciez, D. Kenne and A. Sommariva).
   
   
7. Polynomial-free unisolvence of polyharmonic splines with odd exponent by random sampling, Dolomites Res. Notes Approx. (DRNA) 17 (2024), 45--47 (with A. Sommariva).
   
   
8. Homogenization of composite materials reinforced with unidirectional fibres with complex curvilinear cross section: a virtual element approach, AIMS Math. Eng. 6 (2024), 510--535 (with E. Artioli, G. Elefante and A. Sommariva).
   
   
9. Unisolvence of random Kansa collocation by Thin-Plate Splines for the Poisson equation, Eng. Anal. Bound. Elem. 165 (2024), 105773 (with F. Dell'Accio and A. Sommariva).
   
   
10. Qsurf: compressed QMC integration on parametric surfaces, JAS - J. Approx. Software 1, 1 (2024) (with G. Elefante and A. Sommariva).
    
    
11. Tchakaloff-like compression of QMC volume and surface integration on the union of balls, Calcolo 61, 46 (2024) (with G. Elefante and A. Sommariva).
    
    
12. A note on polynomial-free unisolvence of polyharmonic splines at random points, Appl. Math. Lett. 157 (2024), 109161 (with L. Bos and A. Sommariva).
    
    
13. Numerical cubature on scattered data by adaptive interpolation, J. Comput. Appl. Math. 444 (2024), 115793 (with R. Cavoretto, A. De Rossi, F. Dell'Accio, F. Di Tommaso, N. Siar and A. Sommariva).
    
    
14. TetraFreeQ: tetrahedra-free quadrature on polyhedral elements, Appl. Numer. Math. 200 (2024), 389--398 (with A. Sommariva).
    
    
15. Chebyshev admissible meshes and Lebesgue constants of complex polynomial projections, J. Comput. Appl. Math. 443 (2024) (with L. Bialas-Ciez, D. Kenne and A. Sommariva).
    
    

    2023

16. Random sampling and unisolvent interpolation by almost everywhere analytic functions, Appl. Math. Lett. 145 (2023) (with F. Dell'Accio and A. Sommariva).
    
    
17. Low-cardinality Positive Interior cubature on NURBS-shaped domains, BIT Numer. Math. 63, 22 (2023) (with A. Sommariva).
    
    

    2022

18. Cubature rules with positive weights on union of disks, Dolomites Res. Notes Approx. DRNA 15 (2022) (Special Issue for the 60th of S. De Marchi, 73--81) (with A. Sommariva).
    
    
19. CQMC: an improved code for low-dimensional Compressed Quasi-MonteCarlo cubature, Dolomites Res. Notes Approx. DRNA 15 (2022) ("Software for Approximation 2022", 92--100) (with G. Elefante and A. Sommariva).
    
    
20. DISC: an adaptive numerical Differentiator by local polynomial Interpolation on SCattered data, Dolomites Res. Notes Approx. DRNA 15 (2022) ("Software for Approximation 2022", 81--91) (with F. Dell'Accio, F. Di Tommaso and N. Siar).
    
    
21. inRS: implementing the indicator function of NURBS-shaped planar domains, Appl. Math. Lett. 130 (2022) (with A. Sommariva).
    
    
22. Near-optimal polynomial interpolation on spherical triangles, Mediterr. J. Math. 19 (2022) (with A. Sommariva).
    
    
23. RBFCUB: a numerical package for near-optimal meshless cubature on general polygons, Appl. Math. Lett. 125 (2022) (with R. Cavoretto, A. De Rossi and A. Sommariva).
    
    
24. Numerical differentiation on scattered data through multivariate polynomial interpolation, BIT Numer. Math. 62 (2022), 773--801 (with F. Dell'Accio, F. Di Tommaso and N. Siar).
    
    

    2021

25. RBF moment computation and meshless cubature on general polygonal regions, Appl. Math. Comput. 409 (2021) (with A. Sommariva).
    
    
26. Numerical hyperinterpolation over spherical triangles, Math. Comput. Simul. 190 (2021), 15--22 (with A. Sommariva).
    
    
27. Near-algebraic Tchakaloff-like quadrature on spherical triangles, Appl. Math. Lett. 120 (2021) (with A. Sommariva).
    
    
28. Computing Tchakaloff-like cubature rules on spline curvilinear polygons, Dolomites Res. Notes Approx. DRNA 14 (2021), 1--11 (with A. Sommariva).
    
    

    2020

29. dCATCH: a numerical package for d-variate near G-optimal Tchakaloff regression via fast NNLS, MDPI-Mathematics 8(7) (2020) - Special Issue "Numerical Methods" (with M. Dessole and F. Marcuzzi).
    
    
30. Quadrature-based polynomial optimization, Optim. Lett. 14 (2020), 1027--1036 (with A. Martinez, F. Piazzon and A. Sommariva).
    co-winner of the OPTL Best Paper Awards for 2020
    
    
31. Near G-optimal Tchakaloff designs, Comput. Statistics 35 (2020), 803--819 (with F. Piazzon and L. Bos).
    
    
32. Accelerating the Lawson-Hanson NNLS solver for large-scale Tchakaloff regression designs, Dolomites Res. Notes Approx. DRNA 13 (2020), 20--29 (with M. Dessole and F. Marcuzzi).
    
    
33. Compressed cubature over polygons with applications to optical design, J. Comput. Appl. Math. 370 (2020) (with B. Bauman and A. Sommariva).
    
    
34. Algebraic cubature on polygonal elements with a circular edge, Comput. Math. Appl. 79 (2020), 2057--2066 (with E. Artioli and A. Sommariva).
    
    

    2019

35. CaTchDes: Matlab codes for Caratheodory-Tchakaloff Near-Optimal Regression Designs, SoftwareX 10 (2019) (with L. Bos).
    
    
36. Near optimal polynomial regression on norming meshes, Sampling Theory and Applications 2019, IEEE Xplore Digital Library (with F. Piazzon and L. Bos).
    
    
37. Chebyshev-Dubiner norming webs on starlike polygons, J. Inequal. Spec. Funct. 10-3 (2019), 26--32.
    
    
38. Tchakaloff polynomial meshes, Ann. Polon. Math. 122 (2019), 221--231 (with L. Bos).
    
    
39. Dubiner distance and stability of Lebesgue constants, J. Inequal. Spec. Funct. 10-2 (2019), 49--60.
    
    
40. Markov inequalities, Dubiner distance, norming meshes and polynomial optimization on convex bodies, Optim. Lett. 13 (2019), 1325--1343 (with F. Piazzon).
    
    

    2018

41. Near optimal Tchakaloff meshes for compact sets with Markov exponent 2, Dolomites Res. Notes Approx. DRNA 11 (2018), 92--96 (Special Issue on Norm Levenberg's 60th birthday).
    
    
42. Subperiodic Dubiner distance, norming meshes and trigonometric polynomial optimization, Optim. Lett. 12 (2018), 1659--1667.
    
    
43. Discrete norming inequalities on sections of sphere, ball and torus, J. Inequal. Spec. Funct. 9-4 (2018), 113--121 (with A. Sommariva).
    
    
44. Nearly optimal nested sensors location for polynomial regression on complex geometries, Sampl. Theory Signal Image Process. 17 (2018), 95--101 (with A. Sommariva).
    
    
45. Global polynomial optimization by norming sets on sphere and torus, Dolomites Res. Notes Approx. DRNA 11 (2018), 10--14.
    
    
46. Stability inequalities for Lebesgue constants via Markov-like inequalities, Dolomites Res. Notes Approx. DRNA 11 (2018), 1--9 (with F. Piazzon).
    
    
47. Subperiodic Trigonometric Hyperinterpolation, "Contemporary Computational Mathematics - 80th of Ian Sloan" (invited paper), Springer, 2018, 283--304 (with G. Da Fies and A. Sommariva).
    
    
48. An elementary approach to polynomial optimization on polynomial meshes, J. Math. Fund. Sci. 50 (2018), 84--91.
    
    
49. A note on total degree polynomial optimization by Chebyshev grids, Optim. Lett. 12 (2018), 63--71 (with F. Piazzon).
    
    

    2017

50. Numerical quadrature on the intersection of planar disks, FILOMAT 31:13 (2017), 4105--4115 (with A. Sommariva).
    
    
51. Subperiodic trigonometric subsampling: a numerical approach, Appl. Anal. Discrete Math. 11 (2017), 470--483 (with A. Sommariva).
    
    
52. Caratheodory-Tchakaloff Least Squares, Sampling Theory and Applications 2017, IEEE Xplore Digital Library (with F. Piazzon and A. Sommariva).
    
    
53. Numerical hyperinterpolation over nonstandard planar regions, Math. Comput. Simulation 141 (2017), 110--120  (with A. Sommariva).
    
    
54. On the use of compressed polyhedral quadrature formulas in embedded interface methods, SIAM J. Sci Comput. 39 (2017), B571-B587 (with Y. Sudhakar, A. Sommariva and W.A. Wall).
    
    
55. Optimal polynomial meshes and Caratheodory-Tchakaloff submeshes on the sphere, Dolomites Res. Notes Approx. DRNA 10 (2017), 18--24 (with P. Leopardi and A. Sommariva).
    
    
56. Caratheodory-Tchakaloff Subsampling, Dolomites Res. Notes Approx. DRNA 10 (2017), 5--14 (with F. Piazzon and A. Sommariva).
    
    
57. Polynomial approximation on Lissajous curves in the d-cube, Appl. Numer. Math. 116 (2017), 47--56 (with L. Bos and S. De Marchi).
    
    
58. Polynomial approximation and quadrature on geographic rectangles, Appl. Math. Comput. 297 (2017), 159--179 (with M. Gentile and A. Sommariva).
    
    
59. Trivariate polynomial approximation on Lissajous curves, IMA J. Numer. Anal., 37 (2017), 519--541 (with L. Bos and S. De Marchi).
    
    

    2016

60. Jacobi norming meshes, Math. Inequal. Appl. 19 (2016), 1089--1095 (with F. Piazzon).
    
    
61. Compressed sampling inequalities by Tchakaloff's theorem, Math. Inequal. Appl. 19 (2016), 395--400.
    
    

    2015

62. Compression of multivariate discrete measures and applications, Numer. Funct. Anal. Optim. 36 (2015), 1198--1223 (with A. Sommariva).
    
    
63. Polynomial fitting and interpolation on circular sections, Appl. Math. Comput. 258 (2015), 410--424 (with A. Sommariva).
    
    
64. Polynomial Meshes: Computation and Approximation, Proceeedings of CMMSE 2015, 414--425, ISBN 978-84-617-2230-3, ISSN 2312-0177 (with S. De Marchi, F. Piazzon and A. Sommariva).
    
    

    2014

65. Sub-optimal polynomial meshes on planar Lipschitz domains, Numer. Funct. Anal. Optim. 35 (2014), 1467--1475 (with F. Piazzon).
    
    
66. Product Gaussian quadrature on circular lunes, Numer. Math. Theory Methods Appl. 7 (2014), 251--264 (with G. Da Fies).
    
    
67. Constructing optimal polynomial meshes on planar starlike domains, Dolomites Res. Notes Approx. DRNA 7 (2014), 22--25 (with F. Piazzon).
    
    
68. Norming meshes by Bernstein-like inequalities, Math. Inequal. Appl. 17 (2014), 929--936.
    
    
69. Multivariate Christoffel functions and hyperinterpolation, Dolomites Res. Notes Approx. DRNA 7 (2014), 26--33 (with S. De Marchi, A. Sommariva).
    
    

    2013

70. On the Lebesgue constant of subperiodic trigonometric interpolation, J. Approx. Theory 167 (2013), 59--64 (with G. Da Fies).
    
    
71. Algebraic cubature by linear blending of elliptical arcs, Appl. Numer. Math. 74 (2013), 49--61 (with G. Da Fies and A. Sommariva).
    
    
72. Small perturbations of polynomial meshes, Appl. Anal. 92 (2013), 1063--1073 (with F. Piazzon).
    
    
73. Polynomial approximation on pyramids, cones and solids of rotation, Dolomites Res. Notes Approx. DRNA 6 (2013), 20--26 (with S. De Marchi).
    
    

    2012

74. On the generation of symmetric Lebesgue-like points in the triangle, J. Comput. Appl. Math. 236 (2012), 4925--4932 (with F. Rapetti, A. Sommariva).
    
    
75. Subperiodic trigonometric interpolation and quadrature, Appl. Math. Comput. 218 (2012), 10630--10638 (with L. Bos).
    
    
76. Trigonometric Gaussian quadrature on subintervals of the period, Electron. Trans. Numer. Anal. 39 (2012), 102--112 (with G. Da Fies).
    
    
77. Algebraic cubature on planar lenses and bubbles, Dolomites Res. Notes Approx. DRNA 5 (2012), 7--12 (with G. Da Fies).
    
    
78. Computing Fekete and Lebesgue points: simplex, square, disk, J. Comput. Appl. Math. 236 (2012), 2477--2486 (with M. Briani, A. Sommariva).
    
    
79. Low cardinality admissible meshes on quadrangles, triangles and disks, Math. Inequal. Appl. 15 (2012), 229--235 (with L. Bos).
    
    
80. The "phase function" method to solve second-order asymptotically polynomial differential equations, Numer. Math. 121 (2012), 565--586 (with R. Spigler).
    
    

    2011

81. Geometric Weakly Admissible Meshes, Discrete Least Squares Approximations and Approximate Fekete Points, Math. Comp. 80 (2011), 1601--1621 (with L. Bos, J.P. Calvi, N. Levenberg, A. Sommariva).
    
    
82. On Multivariate Newton Interpolation at Discrete Leja Points, Dolomites Res. Notes Approx. DRNA 4 (2011), 15--20 (with L. Bos, S. De Marchi, A. Sommariva).
    
    
83. Polynomial interpolation and cubature over polygons, J. Comput. Appl. Math. 235 (2011), 5232--5239 (with M. Gentile, A. Sommariva).
    
    
84. An algebraic cubature formula on curvilinear polygons, Appl. Math. Comput. 217 (2011), 10003--10015 (with G. Santin, A. Sommariva).
    
    
85. Padua2DM: fast interpolation and cubature at the Padua points in Matlab/Octave, Numer. Algorithms 56 (2011), 45--60 (with M. Caliari, S. De Marchi, A. Sommariva).
    
    
86. Weakly Admissible Meshes and Discrete Extremal Sets, Numer. Math. Theory Methods Appl. 4 (2011), 1--12 (with L. Bos, S. De Marchi, A. Sommariva).
    
    

    2010

87. Computing multivariate Fekete and Leja points by numerical linear algebra, SIAM J. Numer. Anal. 48 (2010), 1984--1999 (with L. Bos, S. De Marchi, A. Sommariva).
    
    
88. Analytic transformations of admissible meshes, East J. Approx. 16 (2010), 313--322 (with F. Piazzon).
    
    
89. Least-squares polynomial approximation on weakly admissible meshes: disk and triangle, J. Comput. Appl. Math. 235 (2010), 660--668 (with L. Bos, A. Sommariva).
    
    
90. On simple approximations to simple curves, Dolomites Res. Notes Approx. DRNA 3 (2010), 1--6 (with L. Bos).
    
    
91. Approximate Fekete points for weighted polynomial interpolation, Electron. Trans. Numer. Anal. 37 (2010), 1--22 (with A. Sommariva).
    
    

    2009

92. Gauss-Green cubature and moment computation over arbitrary geometries, J. Comput. Appl. Math. 231 (2009), 886--896 (with A. Sommariva).
    
    
93. A numerical code for fast interpolation and cubature at the Padua points, Proceedings of the 9th CMMSE (2009), Vol. I, 218--228 (with M. Caliari, S. De Marchi, A. Sommariva).
    
    
94. A massively parallel exponential integrator for advection-diffusion models, J. Comput. Appl. Math. 231 (2009), 82--91 (with L. Bergamaschi, M. Caliari, A. Martinez).
    
    
95. Computing approximate Fekete points by QR factorizations of Vandermonde matrices, Comput. Math. Appl. 57 (2009), 1324--1336 (with A. Sommariva).
    
    
96. New cubature formulae and hyperinterpolation in three variables, BIT Numerical Mathematics 49 (2009), 55--73 (with S. De Marchi, Y. Xu).
    
    

    2008

97. Algorithm 886: Padua2D: Lagrange Interpolation at Padua Points on Bivariate Domains, ACM Trans. Math. Software 35-3 (2008) (with M. Caliari, S. De Marchi).
    
    
98. Nontensorial Clenshaw-Curtis cubature, Numer. Algorithms 49 (2008), 409--427 (with A. Sommariva, R. Zanovello).
    
    
99. Hyperinterpolation in the cube, Comput. Math. Appl. 55 (2008), 2490--2497 (with M. Caliari, S. De Marchi).
    
    
100. Bivariate Lagrange interpolation at the Padua points: computational aspects, J. Comput. Appl. Math. 221 (2008), 284--292 (with M. Caliari, S. De Marchi).
     
     
101. Meshless cubature over the disk by Thin-Plate Splines, J. Comput. Appl. Math. 221 (2008) 430--436 (with A. Punzi and A. Sommariva).
     
     
102. Asymptotic approximations for second-order linear difference  equations in Banach algebras, II, J. Math. Anal. Appl. 340 (2008), 433--450 (with T. Solda`, R. Spigler).
     
     
103. Asymptotic approximations for second-order linear difference equations in Banach algebras, I, J. Math. Anal. Appl. 337 (2008), 1158--1170 (with T. Solda`, R. Spigler).
     
     

     2007

104. Bivariate Lagrange interpolation at the Padua points: the ideal theory approach, Numer. Math. 108 (2007), 43--57 (with L. Bos, S. De Marchi, Y. Xu).
     
     
105. Product Gauss cubature over polygons based on Green's integration formula, BIT Numerical Mathematics 47 (2007), 441--453 (with A. Sommariva).
     
     
106. The LEM exponential integrator for advection-diffusion-reaction equations, J. Comput. Appl. Math. 210 (2007), 56--63 (with L. Bergamaschi, M. Caliari).
     
     
107. Hyperinterpolation on the square, J. Comput. Appl. Math. 210 (2007), 78--83 (with M. Caliari, S. De Marchi).
     
     
108. Liouville-Green asymptotic approximation for a class of matrix differential equations and semi-discretized partial differential equations, J. Math. Anal. Appl. 325 (2007), 69--89 (with R. Spigler).
     
     

     2006

109. Bivariate Lagrange interpolation at the Padua points: the generating curve approach, J. Approx. Theory 143 (2006), 15--25 (with L. Bos, M. Caliari, S. De Marchi, Y. Xu).
     
     
110. Meshless cubature by Green's formula, Appl. Math. Comput. 183 (2006), 1098--1107 (with A. Sommariva).
     
     
111. Hyper2d: a numerical code for hyperinterpolation on rectangles, Appl. Math. Comput. 183 (2006), 1138--1147 (with M. Caliari, S. De Marchi, R. Montagna).
     
     
112. Bivariate interpolation at Xu points: results, extensions and applications, Electron. Trans. Numer. Anal. 25 (2006), 1--16 (with L. Bos, M. Caliari, S. De Marchi).
     
     
113. On the Lebesgue constant for the Xu interpolation formula, J. Approx. Theory 141 (2006), 134--141 (with L. Bos, S. De Marchi).
     
     
114. Comparing Krylov and Leja approximations of large scale matrix exponentials, Springer LNCS vol. 3994, part IV, 2006,  685-692 (with L. Bergamaschi, M. Caliari, A. Martinez).
     
     
115. A numerical study of the Xu polynomial interpolation formula in two variables, Computing 76 (2006), 311--324 (with L. Bos, M. Caliari, S. De Marchi).
     
     
116. Numerical cubature on scattered data by radial basis functions, Computing 76 (2006), 295--310 (with A. Sommariva).
     
     
117. Liouville-Green asymptotics for almost-diagonal second-order matrix differential equations, Asymptotic Analysis 48 (2006), 267--294 (with R. Spigler).
     
     

     2005

118. Bivariate polynomial interpolation on the square at new nodal sets, Appl. Math. Comput. 165 (2005), 261--274 (with M. Caliari, S. De Marchi).
     
     
119. Adaptive bivariate Chebyshev approximation, Numer. Algorithms 38 (2005),  79--94 (with A. Sommariva, R. Zanovello).
     
     
120. A parallel exponential integrator for large-scale discretizations of advection-diffusion models, Springer LNCS vol. 3666, 2005, 483-492 (with L. Bergamaschi, M. Caliari, A. Martinez).
     
     

     2004

121. The ReLPM exponential integrator for FE discretizations of advection-diffusion equations, Springer LNCS vol. 3039, part IV, 2004, 434--442 (with L. Bergamaschi, M. Caliari).
     
     
122. Adaptive bivariate Chebyshev approximation and efficient evaluation of integral operators, Appl. Numer. Anal. Comput. Math. 1 (2004), 115--121 (with A. Mardegan, A. Sommariva, R. Zanovello).
     
     
123. Interpolating discrete advection-diffusion propagators at Leja sequences, J. Comput. Appl. Math. 172 (2004), 79--99 (with L. Bergamaschi, M. Caliari).
     
     

     2003

124. Fast evaluation of discrete integral transforms by Chebyshev and Leja polynomial approximation, Constructive theory of functions, 347--353, DARBA, Sofia, 2003 (with S. De Marchi).
     
     
125. Efficient approximation of the exponential operator for discrete 2D advection-diffusion problems, Numer. Linear Algebra Appl. 10 (2003), 271--289 (with L. Bergamaschi, M. Caliari).
     
     

     2001

126. Approximating the approximant: a numerical code for polynomial compression of discrete integral operators, In memory of W. Gross. Numer. Algorithms 28 (2001),  101--116 (with S. De Marchi).
     
     
127. Fast summation of power series with coefficients analytic at infinity, Numer. Algorithms 27 (2001), 77--87 (with A. Sommariva, R. Zanovello).
     
     
128. Positive multiplication preserves dissipativity in commutative C*-algebras, J. Inequal. Appl. 6 (2001), 247--251 (with A. Sommariva).
     
     

     2000

129. Chebyshev-like compression of linear and nonlinear discretized integral operators, Neural Parallel Sci. Comput. 8 (2000), 327--353.
     
     
130. Computing positive fixed-points of decreasing Hammerstein operators by relaxed iterations, J. Integral Equations Appl. 12 (2000), 95--112 (with A. Sommariva).
     
     
131. Relaxed Picard-like methods for nonlinear integral equations arising in transport theory, Proc. of Venice2: Appl. and Ind. Math., 1998, 273--285, Kluwer, 2000 (with E. Facchinello, A. Sommariva).
     
     
132. Efficient computation of the exponential operator for large, sparse, symmetric matrices, Numer. Linear Algebra Appl. 7 (2000), 27--45 (with L. Bergamaschi).
     
     
133. A new summation method for power series with rational coefficients, Math. Comp. 69 (2000), 749--756 (with S. Dassie`, R. Zanovello).
     
     
134. A variant of the complex Liouville-Green approximation theorem, Arch. Math. (Brno) 36 (2000), 213--218 (with R. Spigler).
     
     
135. Existence of positive continuous solutions of perturbed Hammerstein equations, Appl. Anal. 74 (2000), 429--438.
     
     
136. Constructive approximation for a class of perturbed Hammerstein integral equations, Nonlinear Anal. 41 (2000), Ser. A: Theory Methods, 177--185 (with A. Sommariva).
     
     

     1999

137. Liouville-Green-Olver approximations for complex difference equations, J. Approx. Theory 96 (1999), 301--322 (with F. Locatelli, R. Spigler).
     
     
138. Constructive analysis of purely integral Boltzmann models, J. Integral Equations Appl. 11 (1999), 393--404 (with A. Sommariva).
     
     
139. On the complex differential equation Y"+G(z)Y=0 in Banach algebras, Stud. Appl. Math. 102 (1999), 291--308 (with R. Spigler).
     
     

     1998

140. Asymptotic summation of power series, Numer. Math. 80 (1998), 61--73 (with S. Dassie`, R. Zanovello).
     
     
141. Approximating fixed-points of decreasing operators in spaces of continuous functions, Numer. Funct. Anal. Optim. 19 (1998), 635--646 (with A. Sommariva).
     
     
142. A survey on the Liouville-Green (WKB) approximation for linear difference equations of the second order, Proc. of ICDEA 1995, 567--577, CRC Press, 1998 (with R. Spigler).
     
     

     1997

143. Peano's kernel theorem for vector-valued functions: a weak version in normed spaces, Numer. Funct. Anal. Optim. 18 (1997), 65--74 (with S. De Marchi).
     
     

     1996

144. Peano's kernel theorem for vector-valued functions and some applications, Numer. Funct. Anal. Optim. 17 (1996), 57--64 (with S. De Marchi).
     
     
145. Asymptotic representation for the Blumenthal-Nevai orthogonal polynomials in the essential spectrum, Methods Appl. Anal. 3 (1996), 457--475 (with R. Spigler).
     
     
146. WKB-type approximations for second-order differential equations in C*-algebras, Proc. Amer. Math. Soc. 124 (1996), 1763--1771 (with R. Spigler).
     
     

     1995

147. Convergence analysis of the semi-implicit Euler method for abstract evolution equations, Numer. Funct. Anal. Optim. 16 (1995), 785--803 (with R. Spigler).
     
     
148. On some connections between well-posedness and general properties of numerical methods, Z. Angew. Math. Mech. 75 (1995), 237--241 (with R. Zanovello).
     
     
149. On regularity at t=0 for semilinear ADEs and its numerical applications, Semigroup Forum 50 (1995),  97--104.
     
     
150. Splitting functions and numerical analysis of WR-type methods for evolutionary and stationary problems, Proc. Sympos. Appl. Math., 48, AMS, 1995 (with S. De Marchi, R. Zanovello).
     
     

     1994

151. Semi-implicit discretization of abstract evolution equations, Equadiff 8 (Bratislava, 1993), Tatra Mt. Math. Publ. 4 (1994), 207--212 (with R. Spigler).
     
     
152. Discrete and continuous Liouville-Green-Olver approximations: a unified treatment via Volterra-Stieltjes integral equations, SIAM J. Math. Anal. 25 (1994), 720--732 (with R. Spigler).
     
     

     1993

153. Cesaro's theorems for complex sequences, J. Math. Anal. Appl. 180 (1993), 317--324 (with R. Spigler).
     
     
154. Abstract versions of L'Hopital's rule for holomorphic functions in the framework of complex B-modules, J. Math. Anal. Appl. 180 (1993), 17--28 (with R. Spigler).
     
     
155. Extending L'Hopital's theorem to B-modules, J. Math. Anal. Appl. 179 (1993), 638--645 (with R. Spigler).
     
     
156. Finite moments perturbations of y"=0 in Banach algebras, Proc. Amer. Math. Soc. 119 (1993), 97--103 (with R. Spigler).
     
     
157. A generalization of l'Hopital's rule via absolute continuity and Banach modules, Real Anal. Exchange 18 (1992/93), 557--567.
     
     

     1992

158. Extensions and numerical applications of the Liouville-Green approximation, Ph.D. Thesis, Univ. of Padova, 1992, 1--84.
     
     
159. On the superlinear convergence of the secant method, Amer. Math. Monthly 99 (1992), 758--761  (with R. Zanovello).
     
     
160. Liouville-Green approximations for a class of linear oscillatory difference equations of the second order, J. Comput. Appl. Math. 41 (1992), 105--116 (with R. Spigler).
     
     
161. Improved estimates for the derivatives of the O-symbols in view of numerical applications, J. Math. Anal. Appl. 164 (1992), 480--488 (with R. Spigler).
     
     
162. WKBJ-type approximation for finite moments perturbations of the differential equation y"=0 and the analogous difference equation, J. Math. Anal. Appl. 169 (1992), 437--452 (with R. Spigler).
     
     

     1991

163. Global existence and uniqueness for the Kummer transformation problem subject to non-Cauchy data, Differential Integral Equations 4 (1991), 991--1003 (with R. Spigler).
     
     

     1990

164. A numerical method for evaluating zeros of solutions of second-order linear differential equations, Math. Comp. 55 (1990), 591--612 (with R. Spigler).
     
     
165. Approximating zeros of solutions of second-order linear ODEs by "phase function" methods, Lecture Notes in Pure and Appl. Math. vol. 124, Dekker, New York, 1990 (with R. Spigler).
     

Didactic curriculum

at the University of Padova, from 1991

Teaching (91 courses)
(o): full course responsibility
(%): teaching assistantship or co-teaching

at the Faculty of Science

• Calcolo Numerico (Numerical Computing) (1st degree in Mathematics, in some years with 2nd degree in Astronomy and in Geology)
  (o) 20 years (1998/99, 2002/03--2016/17, 2019/20--2021/22, 2024/25) and (%) 6 years (1994/95, 1995/96, 1997/98, 1999/00, 2000/01, 2017/18)
  
  
• Calcolo Numerico (Numerical Computing) (1st degree in Computer Science)
  (o) 13 years (2003/04--2009/10, 2013/14, 2019/20--2023/24)
  
  
• Didattica del Calcolo Numerico (Teaching Numerical Computing) (training and refresher course for high-school teachers
  Master program "Methodology and Didactics of Mathematics")
  (o) 8 years (2001/02--2005/06, 2011/12--2013/14)
  
  
• Analisi Numerica (Numerical Analysis) (2nd degree in Mathematics)
  (o) 6 years (2002/03, 2004/05, 2006/07, 2007/08, 2010/11, 2011/12) and (%) 5 years (1997/98, 1998/99, 2008/09, 2009/10, 2012/13)
  
  
• Calcolo Numerico e Programmazione (Numerical Computing and Computer Programming) (2nd degree in Astronomy)
  (o) 5 years (2013/14--2017/18)
  
  
• Elementi di Calcolo Numerico (Elements of Numerical Computing) (1st degree in Materials Science)
  (o) 3 years (2001/02--2003/04)
  
  
• Calcolo Numerico e Programmazione (Numerical Computing and Computer Programming) (1st degree in Chemistry)
  (o) 2 years (2000/01, 2001/02) and (%) 3 years (1996/97, 1998/99, 1999/00)
  
  
• Complementi di Calcolo Numerico (Advanced Numerical Computing) (2nd degree in Computer Science)
  (o) 2 years (2004/05, 2005/06)
  
  
• Calcolo Numerico e Programmazione (Numerical Computing and Computer Programming) (1st degree in Materials Science)
  (%) 2 years (1998/99, 1999/00)
  
  
• Istituzioni di Analisi Superiore (Real Analysis) (2nd degree in Mathematics)
  (%) 2 years (1993/94, 1994/95)
  
  
• Introduzione al Calcolo Numerico (Introductory Numerical Computing) (1st degree in Astronomy)
  (o) 2 years (2022/23--2023/24)
  
  

at the Faculty of Engineering

• Calcolo Numerico (Numerical Computing) (1st degree in Industrial Engineering and in Energy Engineering)
  (o) 9 years (2012/13, 2014/15, 2016/17, 2017/18, 2019/20, 2021/22--2024/25) and (%) 1 year (2020/21)
  
  
• Analisi 2 (Analysis 2) (1st degree in Electrical Engineering)
  (%) 2 years (1991/92, 1992/93)
  
  

Written tutorials (in Italian)

• 24 Lectures on Numerical Computing (handwritten, available online to the students)
  Ch. 1: numbers, floats 1-2, operations, subtraction, propagation, complexity
  Ch. 2: bisection, Newton 1-2, fixed-point
  Ch. 3: interpolation 1-2, piecewise interpolation, least squares
  Ch. 4: quadrature, differentiation, extrapolation
  Ch. 5: vector & matrix norms, conditioning, Gaussian elimination 1-2-3, overdetermined systems and QR
  
  
• Traces of numerical computing
  
  
• Traces of numerical analysis
  
  
• Exercises and complements of functional analysis
  
  
• Exercises and complements of measure and integration theory
  
  

Ph.D. courses

• Teoria dell'Approssimazione Polinomiale (Polynomial Approximation Theory) (Ph.D. program in Computational Mathematics)
  (o) 3 years (2006/07--2008/09)
  
  

Mini-course on didactics

• Fundamentals of numerical computing (fall 2000)
  2 lectures for the Padova section of the Mathesis (association of the high-school teachers in mathematics)
  
  

Supervision and organization

• Advisor of 3 Ph.D.s at the Doctoral School in Mathematics (Curriculum in Computational Mathematics) of the University of Padova:
  Alvise Sommariva 1999 (presently associate professor at the University of Padova), Marco Caliari 2002 (presently associate professor at the University of Verona),
  Federico Piazzon 2016 (presently RTDA lecturer at the University of Padova), see also The Mathematics Genealogy Project
  
  
• Supervisor of 37 "laurea" theses for the degrees in Mathematics (23 Master and 14 Batchelor dissertations), most of type "research thesis" in numerical analysis
  (10 theses have led to scientific publications in collaboration)
  
  
• Supervisor of 21 final theses of high-school teachers for the Master program in "Methodology and Didactics of Mathematics"
  
  
• Member of the Board for didactics (Commissione Didattica) of the degrees in Mathematics (2002-2004, 2012-2013 and 2019-)
  
  
• Member of the Board of the Doctoral School in Mathematics (Curriculum in Computational Mathematics) of the University of Padova (2005-2010 and 2019-2020)