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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
northeastern
universities consortium: BolognaPadovaTriesteUdine)
with the
thesis Extensions and numerical applications of the LiouvilleGreen
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 (since October 2000)
 National scientific qualification (Abilitazione Scientifica
Nazionale) as full professor of Numerical
Analysis, December 2013December 2019
 National scientific qualification (Abilitazione Scientifica
Nazionale) as full professor of Numerical
Analysis, May 2019May 2025
Research results
Author of
 over
130 mathematical papers
in the fields of:
Multivariate Approximation Theory and Algorithms 
Numerical Quadrature and Cubature
Numerical Methods
for Differential and Integral Equations  Asymptotic
Approximations
with 27 coauthors,
published
in 57 international journals and book series
 several
software packages
main areas
 Multivariate Approximation: Polynomial Fitting, Numerical
Cubature, Polynomial Inequalities, Polynomial Optimization
(78 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
some selected papers

the Real Leja Points exponential integrator for
advectiondiffusion equations
Interpolating discrete advectiondiffusion propagators at Leja sequences
with L. Bergamaschi, M. Caliari
J. Comput. Appl. Math. 172 (2004), 7999

Padua Points: discovery of the first optimal point set
for multivariate polynomial interpolation
Bivariate polynomial interpolation on the square at new nodal sets
with M. Caliari, S. De Marchi
Appl. Math. Comput. 165/2 (2005), 261274

nearoptimal multivariate interpolation points by basic Numerical
Linear
Algebra
Computing approximate Fekete points by QR factorizations of
Vandermonde matrices
with A. Sommariva
Comput. Math. Appl. 57 (2009), 13241336

one of the recent approaches to Subperiodic Harmonic
Analysis
Subperiodic trigonometric interpolation and quadrature
with L. Bos
Appl. Math. Comput. 218 (2012), 1063010638

one of the first multivariate implementations of
Tchakaloff Theorem
Compression
of multivariate discrete
measures and
applications
with A. Sommariva
Numer. Funct. Anal. Optim. 36 (2015), 11981223

the first connection of the notions of Dubiner Distance and
Norming Mesh to Polynomial Optimization
A note on total degree polynomial optimization by Chebyshev grids
with F. Piazzon
Optim. Lett. 12 (2018), 6371

the first connection of Quadrature Theory to Polynomial
Optimization Theory
Quadraturebased polynomial optimization
with A. Martinez, F. Piazzon, A. Sommariva
Optim. Lett. (2019), to appear
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 353 (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 LargeScale Simulations Using
Gaussian Basis Sets, J. Chem. Theory Comput. 5, 2009)

GaussGreen cubature and moment computation over arbitrary geometries,
J. Comput. Appl. Math. 231 (2009)
(with A. Sommariva)
the Matlab code has been used in the CFD package
SADoRe: Highly Accurate
Lagrangian Flux Calculation
via Algebraic Quadratures
on SplineApproximated 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 ParksMcClellan
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
finiteelement research
code BACI
developed at
the
Institute for Computational Mechanics, TUM Muenchen
(cf.
paper 112 in the list below)
Research collaboration and coordination experience
 Cofounder of the
CAA: PadovaVerona Research Group on Constructive Approximation and
Applications
 Member of the national research network:
RITA
(Rete ITaliana di Approssimazione)
 International collaborations
(visits, coauthorship,
research projects, ...) with
Brian Bauman (LLNL, USA),
Len Bos (Calgary, Verona 2009),
JeanPaul Calvi (Toulouse),
Mahadevan Ganesh (Colorado School of Mines, Golden),
Paul Leopardi (Melbourne),
Norm Levenberg (Bloomington),
Francesca Rapetti (Nice),
Ian Sloan (UNSW, Sydney),
Shayne Waldron (Auckland),
Yuan Xu (Eugene)

Coautorship with 27 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 (presently associate professor at the
University of Padova),
Marco Caliari 2002 (presently associate professor at the
University of Verona),
Federico Piazzon 2016 (presently PostDoc at the
University of Padova), see also The
Mathematics Genealogy
Project

Supervisor of 4 postdoc fellowships at the Dept. of Mathematics
of the University of Padova:
Alvise Sommariva 20002004,
Angeles
Martinez 20052006 (presently RTDB lecturer of numerical
analysis at the University of Trieste),
Marco Caliari 20062007 and
Federico Piazzon 20172019
 Supervisor of 10 "laurea" theses
for the degrees in Mathematics, that have led to 19 scientific
publications
in collaboration with the students
 Coordinator
of a Padova University project on "Efficient approximation methods for
nonlocal discrete transforms" (20032004, 35 kEuros,
8 members)
 Local coordinator of a PRIN 2003 national project on
"Approximation
of matrix functions in the numerical solution of differential
equations"
(20042005, national coordinator L. Lopez, Bari;
peerreview score 90/100, 28 kEuros, 4 members)
 Coordinator
of 14 local annual projects on topics of multivariate approximation
and applications
(years 20052018, about 3 kEuros and 3 members per year)
 Coordinator of the research group
DOR1951457/19 "Multivariate Approximation for Computational
Optics, Geospatial Analysis and Numerical Modelling"
at the
Dept. of Mathematics of the University of Padova
 Local coordinator of a PRIN 2009 national project on
"Locating nearoptimal nodal sets for multivariate interpolation"
(national coordinator L. Bos, Verona; peerreview score 95/100, not
funded)
 National coordinator of a PRIN 2011 national project on
"Multivariate Interpolation by Polynomials, RBF and other Bases
and Applications"
(preselection peerreview score 98/100, not funded in the
national selection)
 Coordinator
of a INdAMGNCS annual project on "Multivariate approximation by
polynomial and radial bases"
(2012, 5 kEuros, 5 members)
 Coresponsible for the funds
of a INdAMGNCS annual project on "Multivariate approximation: theory
and applications"
(JulyDec. 2017, 7.8 kEuros, 14 members)
 Scientific responsible of a postdoc fellowship project
on "Numerical Modelling by CaratheodoryTchakaloff Quadrature
Compression"
at the Dept. of Mathematics of the University of Padova
(2019, peerreview score 97/100)
 Member of the Scientific board (Commissione Scientifica)
for research in Mathematics
and Computer Science, University of Padova (20042005)
 Member of the Board of the Doctoral School in
Mathematics (Curriculum in Computational Mathematics) of the University of
Padova (20052010)
 Member of the Board of the Doctoral School in
Mathematics of the University of
Padova (2019)
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. 812 2006
2nd Dolomites Workshop on
Constructive Approximation and Applications (DWCAA09),
Alba di Canazei
(Trento, Italy), Sept. 49 2009
3rd Dolomites Workshop on
Constructive Approximation and Applications (DWCAA12),
Alba di Canazei
(Trento, Italy), Sept. 914 2012
4th Dolomites Workshop on
Constructive Approximation and Applications (DWCAA16),
Alba di Canazei
(Trento, Italy), Sept. 813 2016
 Member of the
scientific committee of
New Trends in Numerical Analysis 
Theory, Methods, Algorithms and Applications (NETNA2015),
Falerna (CZ), Italy, June 1821 2015
 Member of the organizing committees of
Dolomites Research Week on Approximation 2007 (DRWA07),
Alba di Canazei
(Trento, Italy), Sept. 37 2007
Dolomites Research Week on Approximation 2008 (DRWA08),
Alba di Canazei
(Trento, Italy), Sept. 811 2008
Dolomites Research Week on Approximation 2010 (DRWA10),
Alba di Canazei
(Trento, Italy), Sept. 610 2010
Dolomites Research Week on Approximation 2011 (DRWA11),
Alba di Canazei
(Trento, Italy), Sept. 59 2011
Dolomites Research Week on Approximation 2013 (DRWA13),
Alba di Canazei
(Trento, Italy), Sept. 913 2013
Workshop on
Multivariate Approximation
celebrating Prof. Len Bos 60th birthday,
Verona (Italy), Nov. 2930 2013
Dolomites Research Week on Approximation 2014 (DRWA14),
Alba di Canazei
(Trento, Italy), Sept. 812 2014
Dolomites Research Week on Approximation 2015 (DRWA15),
Alba di Canazei
(Trento, Italy), Sept. 58 2015
Dolomites Research Week on Approximation 2017 (DRWA17),
Alba di Canazei
(Trento, Italy), Sept. 48 2017
Approssimazione Multivariata: Teoria ed Applicazioni (AMTA 2017),
Palermo, Italy, Dec. 810 2017
Dolomites Research Week on Approximation 2018 (DRWA18),
Alba di Canazei
(Trento, Italy), Sept. 1014 2018
 Managing Editor of the electronic journal
Dolomites Research Notes on Approximation
indexed in
DOAJ //
EMIS //
MathSciNet //
Scopus //
Web of Science //
Zentralblatt
 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 Committee for the selection of
postdoc fellowship projects at the Dept. of Mathematics
of the University of Padova (2012)
 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  Flanders, Belgium (20132015)
 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)
 Member of the Committee for the selection of
research and
postdoc fellowship projects at the Dept. of Mathematics
of the University of Padova (2017)
 Member of the Committees for the selection of
two postdoc positions in numerical analysis at the Dept. of Mathematics
of the University
of Padova (Nov. 2017 and April 2018)
 Member of the Committee for the selection of
senior postdoc fellowship projects at the Dept. of Mathematics
of the University of Padova (Sept.Oct. 2018)
 Project reviewer for the
National Research, Development and
Innovation Office of Hungary, Panel "Mathematics and
Computer Science" (2018)
 Project reviewer for the
Austrian Science Fund (FWF) (2018)
 Referee selected by 40 international journals:
* Advances in
Computational
Mathematics
* Advances in Difference
Equations
* Annales Polonici Mathematici
* Applied
Mathematics and Computation *
* Applied Numerical Mathematics
* BIT Numerical Mathematics
* Bollettino dell'Unione Matematica Italiana
* 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 *
* 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 *
* Journal of Approximation Theory
* Journal of Computational and Applied
Mathematics
* Journal of Computational Physics *
* Journal of Foundations of Computational Mathematics
* 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
* Rendiconti di Matematica e delle sue Applicazioni *
* Statistics and Computing
* SIAM Journal on Numerical Analysis
* SIAM Journal on Scientific Computing
* Vietnam Journal of Mathematics *
5 selected presentations at international conferences

"A vectorvalued
version of Peano's Kernel Theorem"
3rd Intern. Conf. on
Functional Anal. and Approx. Theory (FAAT 1996), Maratea
(Italy) Sept. 1996

"Nearoptimal
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 CaratheodoryTchakaloff Points"
2nd Joint Meeting SpainBrazil in Mathematics,
Cadiz (Spain) Dec. 2018
Complete list of mathematical publications
2019

Near Goptimal Tchakaloff designs,
Comput. Statistics, accepted after minor revision (with
F. Piazzon and L. Bos).

ChebyshevDubiner norming webs
on starlike polygons,
J. Inequal. Spec. Funct., to appear.

Near optimal polynomial regression on norming meshes,
Sampling Theory and Applications 2019, IEEE Xplore Digital Library,
to appear (with
F. Piazzon and L. Bos).

Tchakaloff polynomial meshes,
Ann. Polon. Math., to appear (with L. Bos).

Dubiner
distance and stability of Lebesgue constants,
J. Inequal. Spec. Funct., published online 2019.

Quadraturebased polynomial optimization,
Optim. Lett., online 07 March 2019 (with A. Martinez, F. Piazzon and A.
Sommariva).

Markov inequalities, Dubiner distance, norming meshes and polynomial
optimization on convex bodies,
Optim. Lett., online 01 January 2019 (with F. Piazzon).
2018

Near optimal Tchakaloff meshes for compact sets
with Markov exponent 2,
Dolomites Res. Notes Approx. DRNA 11 (2018), 9296
(Special Issue on
Norm Levenberg's 60th birthday).

Subperiodic Dubiner distance, norming meshes and trigonometric
polynomial optimization,
Optim. Lett. 12 (2018), 16591667.

Discrete norming inequalities on sections of sphere, ball and
torus, J. Inequal. Spec. Funct. 9 (2018), 113121 (with A.
Sommariva).

Nearly optimal nested sensors location for polynomial
regression on
complex geometries,
Sampl. Theory Signal Image Process. 17 (2018), 95101
(with A. Sommariva).

Global polynomial optimization by norming sets on sphere and torus,
Dolomites Res. Notes Approx. DRNA 11 (2018), 1014.

Stability inequalities for Lebesgue constants via Markovlike
inequalities,
Dolomites Res. Notes Approx. DRNA 11 (2018), 19 (with F. Piazzon).

Subperiodic
Trigonometric Hyperinterpolation,
in: "Contemporary Computational Mathematics  a celebration of
the 80th birthday
of Ian Sloan"
(invited paper), J. Dick, F.Y.
Kuo, H. Wozniakowski Eds., Springer, 2018, pp. 283304
(with G. Da Fies and A. Sommariva).

An elementary approach to polynomial optimization on polynomial
meshes,
J. Math. Fund. Sci. 50 (2018), 8491.

A note on total degree polynomial optimization by Chebyshev grids,
Optim. Lett. 12 (2018), 6371 (with F. Piazzon).
2017
 Numerical
quadrature on the intersection of planar disks,
FILOMAT 31:13 (2017), 41054115 (with A. Sommariva).

Subperiodic
trigonometric subsampling: a numerical approach,
Appl. Anal. Discrete Math. 11 (2017), 470483 (with A. Sommariva).
 CaratheodoryTchakaloff Least Squares,
2017 International Conference on Sampling Theory and Applications
(SampTA),
IEEE Xplore Digital Library, DOI: 10.1109/SAMPTA.2017.8024337
(with F. Piazzon and A. Sommariva).

Numerical
hyperinterpolation over nonstandard planar regions,
Math. Comput. Simulation 141 (2017), 110120
(with A.
Sommariva).

On the use of compressed polyhedral quadrature formulas in embedded
interface
methods,
SIAM J. Sci Comput. 39 (2017), B571B587
(with Y. Sudhakar, A. Sommariva and W.A. Wall).

Optimal polynomial meshes and CaratheodoryTchakaloff submeshes on
the sphere, Dolomites Res. Notes Approx. DRNA 10 (2017), 1824
(with P. Leopardi and A. Sommariva).
 CaratheodoryTchakaloff Subsampling,
Dolomites Res. Notes Approx. DRNA 10 (2017), 514
(with F. Piazzon and A. Sommariva).

Polynomial approximation on Lissajous curves in the dcube,
Appl. Numer. Math. 116 (2017), 4756
(with L. Bos
and S. De Marchi).
 Polynomial approximation and quadrature on geographic
rectangles, Appl. Math. Comput. 297 (2017), 159179
(with M. Gentile and A. Sommariva).
 Trivariate
polynomial approximation on Lissajous curves, IMA J. Numer.
Anal. 37 (2017), 519541
(with L. Bos and S. De Marchi).
2016
 Jacobi norming meshes,
Math. Inequal. Appl. 19 (2016), 10891095 (with F. Piazzon).
 Compressed
sampling
inequalities by Tchakaloff's theorem,
Math. Inequal. Appl. 19 (2016), 395400.
2015
 Compression of multivariate discrete measures and
applications,
Numer. Funct. Anal. Optim. 36 (2015), 11981223
(with A. Sommariva).
 Polynomial fitting and interpolation on circular sections,
Appl. Math. Comput. 258 (2015), 410424
(with A. Sommariva).
 Polynomial
Meshes: Computation and Approximation, Proceeedings of CMMSE 2015,
414425, ISBN 9788461722303, ISSN 23120177
(with S. De Marchi, F.
Piazzon and A. Sommariva).
2014
 Suboptimal polynomial meshes
on planar Lipschitz domains,
Numer. Funct. Anal. Optim. 35 (2014), 14671475
(with F. Piazzon).
 Product Gaussian quadrature on circular
lunes,
Numer. Math. Theory Methods Appl. 7 (2014), 251264 (with G. Da
Fies).
 Constructing optimal polynomial meshes on planar starlike
domains,
Dolomites Res. Notes Approx. DRNA 7 (2014), 2225 (with F. Piazzon).
 Norming meshes by Bernsteinlike
inequalities, Math. Inequal. Appl. 17 (2014), 929936.
 Multivariate Christoffel functions and hyperinterpolation,
Dolomites Res. Notes Approx. DRNA 7
(2014), 2633 (with S. De Marchi, A.
Sommariva).
2013
 On the Lebesgue constant of subperiodic trigonometric
interpolation,
J. Approx. Theory 167 (2013), 5964 (with G. Da Fies).
 Algebraic cubature by linear blending of
elliptical arcs,
Appl. Numer. Math. 74 (2013), 4961 (with G. Da Fies and
A. Sommariva).
 Small perturbations of polynomial meshes,
Appl. Anal. 92 (2013), 10631073 (with F. Piazzon).
 Polynomial approximation on pyramids, cones
and solids of
rotation,
Dolomites Res. Notes Approx. DRNA 6 (2013), 2026 (with
S. De Marchi).
2012
 Subperiodic trigonometric interpolation and quadrature,
Appl. Math. Comput. 218 (2012), 1063010638 (with L. Bos).
 On the generation of symmetric
Lebesguelike points in the triangle,
J. Comput. Appl. Math. 236 (2012), 49254932
(with F. Rapetti, A. Sommariva).
 Trigonometric Gaussian quadrature on subintervals of
the period, Electron. Trans. Numer. Anal. 39 (2012), 102112
(with G. Da Fies).
 Algebraic cubature on planar lenses and bubbles,
Dolomites Res. Notes Approx. DRNA 5 (2012), 712 (with G. Da Fies).
 Computing Fekete and Lebesgue points: simplex, square,
disk, J. Comput. Appl. Math. 236 (2012), 24772486
(with M. Briani, A.
Sommariva).
 Low cardinality admissible meshes on quadrangles,
triangles and disks, Math. Inequal. Appl. 15 (2012), 229235
(with L. Bos).
 The "phase function" method to solve secondorder
asymptotically polynomial differential equations, Numer. Math.
121 (2012), 565586 (with
R. Spigler).
2011

Geometric Weakly Admissible Meshes, Discrete Least Squares
Approximations and Approximate Fekete Points, Math. Comp. 80 (2011),
16011621
(with L. Bos, J.P. Calvi, N. Levenberg, A.
Sommariva).

On Multivariate Newton Interpolation at Discrete Leja
Points,
Dolomites Res. Notes Approx. DRNA 4 (2011), 1520
(with L. Bos, S. De Marchi, A. Sommariva).

Polynomial interpolation and cubature over polygons,
J. Comput. Appl. Math. 235 (2011), 52325239
(with M. Gentile, A. Sommariva).

An algebraic cubature formula on curvilinear polygons, Appl. Math.
Comput. 217 (2011), 1000310015
(with G. Santin, A. Sommariva).
 Padua2DM: fast interpolation and cubature at the Padua
points in
Matlab/Octave,
Numer. Algorithms 56 (2011), 4560 (with M. Caliari, S. De
Marchi, A.
Sommariva).
 Weakly Admissible Meshes and Discrete Extremal Sets,
Numer. Math. Theory Methods Appl. 4 (2011), 112 (with L. Bos, S. De
Marchi, A. Sommariva).
2010

Computing multivariate Fekete and Leja points by numerical linear
algebra, SIAM J. Numer. Anal. 48 (2010), 19841999 (with L. Bos, S.
De Marchi, A. Sommariva).

Analytic transformations of admissible meshes, East J. Approx.
16 (2010), 313322 (with F. Piazzon).
 Leastsquares polynomial approximation on weakly
admissible
meshes: disk and triangle,
J. Comput. Appl. Math. 235 (2010), 660668 (with L. Bos, A.
Sommariva).

On simple approximations to simple curves,
Dolomites Res. Notes Approx. DRNA 3 (2010), 16
(with L. Bos).

Approximate Fekete points for weighted polynomial interpolation,
Electron. Trans. Numer. Anal. 37 (2010), 122 (with A. Sommariva).
2009
 GaussGreen cubature and moment computation over arbitrary
geometries, J. Comput. Appl. Math. 231 (2009), 886896 (with
A. Sommariva).
 A numerical code for fast interpolation and cubature at the
Padua points, Proceedings of the 9th CMMSE (2009), Vol. I, 218228
(with M. Caliari, S. De Marchi, A. Sommariva).
 A massively parallel
exponential integrator for advectiondiffusion models, J. Comput.
Appl. Math. 231 (2009), 8291 (with L. Bergamaschi, M.
Caliari, A. Martinez).
 Computing approximate Fekete points by QR factorizations of
Vandermonde matrices,
Comput. Math. Appl. 57 (2009), 13241336 (with A.
Sommariva).
 New cubature formulae and hyperinterpolation in three
variables,
BIT Numerical Mathematics 49 (2009), 5573 (with S. De
Marchi, Y. Xu).
2008
 Algorithm 886: Padua2D: Lagrange Interpolation at Padua
Points on Bivariate
Domains, ACM Trans. Math. Software 353 (2008) (with M. Caliari, S.
De Marchi).
 Nontensorial ClenshawCurtis cubature, Numer.
Algorithms 49 (2008), 409427 (with A. Sommariva, R.
Zanovello).
 Hyperinterpolation in the cube, Comput. Math. Appl.
55 (2008), 24902497 (with M. Caliari, S. De
Marchi).
 Bivariate Lagrange interpolation at the Padua points:
computational aspects, J. Comput. Appl. Math. 221 (2008), 284292
(with M. Caliari, S. De Marchi).
 Meshless cubature over the disk by ThinPlate Splines,
J. Comput. Appl. Math. 221 (2008) 430436
(with A. Punzi and A. Sommariva).
 Asymptotic approximations for secondorder linear difference
equations in Banach algebras, II, J. Math. Anal. Appl. 340
(2008), 433450 (with T. Solda`, R. Spigler).
 Asymptotic approximations for secondorder linear difference
equations in Banach algebras, I, J. Math. Anal. Appl. 337 (2008),
11581170 (with T. Solda`, R. Spigler).
2007
 Bivariate Lagrange interpolation at the Padua points:
the ideal theory approach, Numer. Math. 108 (2007), 4357 (with L.
Bos, S. De Marchi, Y. Xu).
 Product Gauss cubature over polygons based on Green's
integration formula,
BIT Numerical Mathematics 47 (2007), 441453
(with A. Sommariva).
 The LEM exponential integrator for
advectiondiffusionreaction
equations, J. Comput. Appl. Math. 210 (2007), 5663 (with L.
Bergamaschi, M. Caliari).
 Hyperinterpolation on the square, J. Comput. Appl.
Math. 210 (2007), 7883 (with M. Caliari, S. De
Marchi).
 LiouvilleGreen asymptotic approximation for a class of
matrix
differential equations and semidiscretized partial differential
equations,
J. Math. Anal. Appl. 325 (2007), 6989 (with R.
Spigler).
2006
 Bivariate Lagrange interpolation at the Padua points: the
generating curve approach, J. Approx. Theory 143 (2006), 1525
(with L. Bos, M. Caliari, S. De Marchi, Y. Xu).
 Meshless cubature by Green's formula, Appl. Math.
Comput. 183 (2006), 10981107 (with A. Sommariva).
 Hyper2d: a numerical code for hyperinterpolation on
rectangles, Appl. Math. Comput. 183 (2006), 11381147
(with M. Caliari, S. De Marchi, R. Montagna).
 Bivariate interpolation at Xu points: results, extensions
and
applications, Electron. Trans. Numer. Anal. 25 (2006), 116
(with L. Bos, M. Caliari, S. De Marchi).
 On the Lebesgue constant for the Xu interpolation
formula,
J. Approx. Theory 141 (2006), 134141 (with L. Bos, S. De Marchi).
 Comparing Krylov and Leja approximations of large scale
matrix
exponentials,
Springer LNCS vol. 3994, part IV, 2006
(Proc. of ICCS 2006, Reading, UK),
685692
(with L. Bergamaschi, M. Caliari, A. Martinez).
 A numerical study of the Xu polynomial interpolation formula
in two variables, Computing 76 (2006), 311324 (with
L. Bos, M. Caliari, S. De Marchi).
 Numerical cubature
on scattered data by radial basis functions,
Computing 76 (2006), 295310 (with A. Sommariva).
 LiouvilleGreen asymptotics for almostdiagonal secondorder
matrix differential equations, Asymptotic Analysis 48 (2006), 267294
(with R. Spigler).
2005
 Bivariate polynomial
interpolation on the square at new nodal sets, Appl. Math. Comput. 165
(2005), 261274 (with M. Caliari, S. De Marchi).
 Adaptive bivariate
Chebyshev approximation, Numer. Algorithms 38 (2005),
7994 (with A. Sommariva, R. Zanovello).
 A parallel exponential integrator for largescale
discretizations of advectiondiffusion models,
Springer LNCS vol. 3666, 2005
(Proc. of Euro PVM MPI 2005,
Sorrento,
Italy), 483492 (with L. Bergamaschi, M. Caliari, A.
Martinez).
2004
 The ReLPM exponential integrator for FE discretizations of
advectiondiffusion equations,
Springer LNCS vol. 3039, part IV, 2004
(Proc. of ICCS 2004,
Krakow,
Poland), 434442 (with L. Bergamaschi, M. Caliari).
 Adaptive bivariate Chebyshev approximation and efficient
evaluation of integral operators,
Appl. Numer. Anal. Comput. Math. 1 (2004), 115121
(with A. Mardegan, A. Sommariva, R. Zanovello).
 Interpolating discrete
advectiondiffusion propagators at Leja sequences, J. Comput. Appl.
Math.
172 (2004), 7999 (with L. Bergamaschi, M.
Caliari).
2003
 Fast evaluation of discrete
integral
transforms by Chebyshev and Leja polynomial approximation,
Constructive
theory of functions, 347353, DARBA, Sofia, 2003
(with
S. De Marchi).
 Efficient approximation of the exponential operator for
discrete 2D
advectiondiffusion problems,
Numer. Linear Algebra Appl. 10 (2003), 271289
(with
L. Bergamaschi, M. Caliari).
2001
 Approximating the
approximant: a
numerical code for polynomial compression of discrete integral
operators,
Numer. Algorithms 28 (2001),
101116 (with S. De Marchi).
 Fast summation of
power series with coefficients analytic at infinity, Numer. Algorithms
27
(2001), 7787 (with A. Sommariva, R. Zanovello).
 Positive multiplication
preserves
dissipativity in commutative C*algebras, J. Inequal. Appl. 6
(2001), 247251 (with A. Sommariva).
2000
 Chebyshevlike compression of linear and
nonlinear
discretized integral operators, Neural Parallel Sci. Comput. 8 (2000),
327353.
 Computing positive
fixedpoints of
decreasing Hammerstein operators by relaxed iterations, J. Integral
Equations Appl. 12 (2000), 95112 (with A.
Sommariva).
 Relaxed
Picardlike
methods
for nonlinear integral equations arising in transport theory, Applied
and
industrial mathematics, Venice2, 1998, 273285,
Kluwer Acad. Publ.,
Dordrecht, 2000 (with E. Facchinello, A. Sommariva).
 Efficient computation of the
exponential operator for large, sparse, symmetric matrices, Numer.
Linear
Algebra Appl. 7 (2000), 2745 (with L.
Bergamaschi).
 A new summation method
for power series with rational coefficients, Math. Comp. 69 (2000),
749756 (with S. Dassie`, R. Zanovello).
 A variant of the complex
LiouvilleGreen
approximation theorem, Arch. Math. (Brno) 36 (2000),
213218 (with R. Spigler).
 Existence of positive continuous solutions of
perturbed
Hammerstein equations, Appl. Anal. 74 (2000),
429438.
 Constructive approximation
for a
class
of perturbed Hammerstein integral equations, Nonlinear Anal. 41
(2000), Ser. A: Theory Methods, 177185 (with A.
Sommariva).
1999
 LiouvilleGreenOlver approximations for complex difference
equations, J. Approx. Theory 96 (1999), 301322
(with F. Locatelli, R. Spigler).
 Constructive analysis of
purely
integral Boltzmann models, J. Integral Equations Appl. 11 (1999),
393404 (with A. Sommariva).
 On the complex differential
equation
Y"+G(z)Y=0 in Banach algebras, Stud. Appl. Math. 102 (1999),
291308 (with R. Spigler).
1998
 Asymptotic summation
of power series, Numer. Math. 80 (1998), 6173
(with S. Dassie`, R. Zanovello).
 Approximating fixedpoints of
decreasing operators in spaces of continuous functions, Numer. Funct.
Anal. Optim. 19 (1998), 635646 (with A.
Sommariva).
 A survey on the
LiouvilleGreen (WKB)
approximation for linear difference equations of the second order,
Advances in Difference Equations:
Proceedings of the Second
International Conference on Difference Equations (Veszprem, 1995),
567577, CRC Press, 1998 (with R. Spigler).
1997
 Peano's kernel theorem for
vectorvalued functions: a weak version in normed spaces, Numer.
Funct.
Anal. Optim. 18 (1997), 6574 (with S. De
Marchi).
1996
 Peano's kernel theorem for
vectorvalued functions and some applications, Numer. Funct. Anal.
Optim.
17 (1996), 5764 (with S. De Marchi).
 Asymptotic representation for
the
BlumenthalNevai orthogonal polynomials in the essential spectrum,
Methods Appl. Anal. 3 (1996), 457475 (with R.
Spigler).
 WKBtype approximations for
secondorder differential equations in C*algebras, Proc. Amer.
Math. Soc. 124 (1996), 17631771 (with R.
Spigler).
1995
 Convergence analysis of the
semiimplicit Euler method for abstract evolution equations,
Numer. Funct. Anal. Optim. 16 (1995), 785803
(with R. Spigler).
 On some connections between
wellposedness
and general properties of numerical methods, Z. Angew. Math. Mech. 75
(1995), 237241 (with R. Zanovello).
 On regularity at t=0 for semilinear ADEs and
its
numerical applications, Semigroup Forum 50 (1995),
97104.
1994
 Splitting functions
and numerical analysis of WRtype methods for evolutionary and stationary
problems,
Mathematics of Computation 19431993: (Vancouver, BC, 1993),
281285, Proc. Sympos.
Appl. Math., 48, AMS, Providence, 1994
(with S. De Marchi, R. Zanovello).
 Semiimplicit discretization
of
abstract
evolution equations, Equadiff 8 (Bratislava, 1993), Tatra Mt. Math.
Publ.
4 (1994), 207212 (with R. Spigler).
 Discrete and continuous
LiouvilleGreenOlver approximations: a unified treatment via
VolterraStieltjes integral equations, SIAM J. Math. Anal. 25 (1994),
720732
(with R. Spigler).
1993
 Cesaro's theorems for complex
sequences,
J. Math. Anal. Appl. 180 (1993), 317324 (with
R. Spigler).
 Abstract versions of
L'Hopital's
rule
for holomorphic functions in the framework of complex Bmodules, J.
Math. Anal. Appl. 180 (1993), 1728 (with R.
Spigler).
 Extending L'Hopital's theorem
to Bmodules, J. Math. Anal. Appl. 179 (1993), 638645
(with R. Spigler).
 Finite moments perturbations of
y"=0 in Banach algebras, Proc. Amer. Math. Soc. 119 (1993),
97103 (with R. Spigler).
 A generalization of l'Hopital's rule via
absolute
continuity and Banach modules, Real Anal. Exchange 18 (1992/93),
557567.
1992
 Extensions and numerical applications of the LiouvilleGreen
approximation, Ph.D. Thesis, Doctoral School in Computational
Mathematics,
Italian NorthEastern Consortium
(Universities of Bologna, Padova, Trieste and Udine), 184
 On the superlinear
convergence of the
secant method, Amer. Math. Monthly 99 (1992), 758761
(with R. Zanovello).
 LiouvilleGreen approximations
for
a class of linear oscillatory difference equations of the second
order,
J. Comput. Appl. Math.
41 (1992), 105116 (with
R. Spigler).
 Improved estimates for the
derivatives
of the Osymbols in view of numerical applications, J. Math. Anal.
Appl.
164 (1992), 480488 (with
R. Spigler).
 WKBJtype approximation for
finite
moments perturbations of the differential equation y"=0 and the
analogous difference equation,
J. Math. Anal. Appl. 169 (1992),
437452 (with
R. Spigler).
1991
 Global existence and uniqueness
for the
Kummer transformation problem subject to nonCauchy data, Differential
Integral Equations 4 (1991), 9911003
(with
R. Spigler).
1990
 A numerical method for
evaluating zeros
of solutions of secondorder linear differential equations, Math.
Comp.
55 (1990), 591612 (with R. Spigler).
 Approximating zeros of solutions of
secondorder linear ODEs by "phase function" methods, Asymptotic and
computational analysis (Winnipeg, MB, 1989), 707722,
Lecture Notes in
Pure and Appl. Math., 124, Dekker, New York, 1990 (with
R. Spigler).
selected citations
citations in books (the numbers refer to the list above)
 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
 69, 80, 84, 85 in: G. Fasshauer and M. McCourt,
Kernelbased
Approximation
Methods using MATLAB, World Scientific, 2015
 20 in: C. Kuhen,
Multiple Time Scale Dynamics, Springer Applied
Mathematical Sciences 191, 2014
 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.,
hpVersion Discontinuous Galerkin Methods on Polygonal and Polyhedral
Meshes, SpringerBriefs in Mathematics, 2017
 90, 95 in:
W. Gautschi,
A Software Repository for Orthogonal
Polynomials, SIAM ebooks, 2018
citations in state of the art surveys
 57 in:
N. Levenberg,
Approximation in C^n, Surveys in Approximation Theory 2
(2006)
 34, 43 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)
 71, 75, 85 in:
S.I. Filip,
A Robust and Scalable Implementation of the ParksMcClellan
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, 127 in: E. de Klerk and M. Laurent,
A survey of semidefinite programming approaches to the generalized
problem
of moments and their error analysis, arXiv: 1811.07677
Didactic curriculum
at the University of Padova, from 1991
Teaching (74 courses)
(o): full course responsibility
(%): teaching assistantship or coteaching
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) 16 years (1998/99, 2002/032016/17) 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) 8 years (2003/042009/10, 2013/14)
 Didattica del Calcolo Numerico (Teaching Numerical
Computing)
(training and refresher course for
highschool
teachers
Master program "Methodology and
Didactics of Mathematics")
(o) 8 years (2001/022005/06, 2011/122013/14)
 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 (2013/142017/18)
 Elementi di Calcolo Numerico (Elements of Numerical Computing)
(1st degree in
Materials Science)
(o) 3 years (2001/022003/04)
 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)
at the Faculty of Engineering
 Calcolo Numerico (Numerical Computing) (1st degree in
Industrial Engineering and in Energy Engineering)
(o) 4 years (2012/13, 2014/15, 2016/17, 2017/18)
 Analisi 2 (Analysis 2) (1st degree in Electrical Engineering)
(%) 2 years (1991/92, 1992/93)
Written tutorials (in Italian)
Ph.D. courses
 Teoria dell'Approssimazione Polinomiale (Polynomial Approximation
Theory)
(Ph.D. program in Computational Mathematics)
(o) 3 years (2006/072008/09)
Talks on didactics
 Fundamentals of numerical computing (fall 2000)
2 talks for the Padova section of the Mathesis
(association of the
highschool 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 PostDoc at the
University of Padova), see also The
Mathematics Genealogy
Project
 Supervisor of 37 "laurea" theses
for the degrees in Mathematics,
most of type
"research thesis" in numerical
analysis
(10 theses have led to scientific publications
in collaboration)
 Supervisor of 21 final theses of highschool teachers
for the Master program
in "Methodology and Didactics of Mathematics"
 Member of the Board for didactics (Commissione Didattica) of
the degrees in
Mathematics (20022004)
 Member of the Board of the Doctoral School in
Mathematics (Curriculum in Computational Mathematics) of the University of
Padova (20052010)
 Member of the Board for didactics (Commissione Didattica) of
the Dept. of Mathematics
(20122013)
 Member of the Board for didactics (Commissione Didattica) of
the Dept. of Mathematics
(2019)
 Member of the Board of the Doctoral School in
Mathematics of the University of
Padova (2019)