Wfilip
Marco Vianello Curriculum
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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, MarylandUSA)
 INdAM research fellowship (Nov. 1991  Aug. 1992, Nov.
1992  Oct. 1993)
 Lecturer of Numerical Analysis at the Faculty of Science
of the University of Padova (December 24, 1993  September 30,
2000)
 Associate professor of Numerical Analysis
at the
Dept. of Mathematics of the University of Padova
(October 1, 2000  April 30, 2017)
 National scientific qualification (Abilitazione Scientifica
Nazionale) as full professor of Numerical
Analysis, December 16, 2013
 Full professor of Numerical Analysis at the
Dept. of Mathematics of the University of Padova (May 1, 2017  present)
Research results
Author of 119 mathematical papers in the fields
of Approximation Theory, Numerical
Analysis and Mathematical Analysis
with 27 coauthors,
published
in 53 international journals and book series, and of
several
software packages, see on the personal web page http://www.math.unipd.it/~marcov
the following:
Topics (with relevant citations in books and state of the
art
surveys; see the complete list of publications below)
1. Multivariate approximation theory: interpolation and least
squares, numerical cubature, polynomial inequalities
(64 papers)
 paper 57 cited in:
N. Levenberg,
Approximation in C^n, Surveys in Approximation Theory 2
(2006)
 papers 48, 57, 62, 69, 71 cited in: T. Bloom, L. Bos, J.P. Calvi and
N. Levenberg,
Polynomial Interpolation
and Approximation in
C^d, Ann. Polon. Math. 106 (2012)
 paper 74 cited in:
Q. Zhang,
On donating regions: Lagrangian flux through a fixed
curve, SIAM Rev. 55 (2013)
 papers 69, 80, 84, 85 cited in: G. Fasshauer and M. McCourt,
Kernelbased
Approximation
Methods using MATLAB, World Scientific, 2015
 papers 71, 75, 85 cited in:
S.I. Filip,
A Robust and Scalable Implementation of the ParksMcClellan
Algorithm for Designing FIR Filters, ACM Trans. Math. Software 43
(2016)
 papers 57, 107 cited in:
L.N. Trefethen,
Cubature, approximation, and isotropy in the hypercube, SIAM Rev. 59
(2017)
 papers 90, 95 cited in:
W. Gautschi, A Software Repository for Orthogonal
Polynomials, SIAM ebooks, to appear
2. Approximation of matrix exponentials and exponential
integrators for ODEs/PDEs (8 papers)
3. Asymptotics/numerics: differential
and difference eqs., fast summation, special functions
(28 papers)
 papers 6, 23, 29 cited in:
NIST Handbook
and Digital Library of
Math. Functions, Chapter 2: Asymptotic Approximations (F.W.J. Olver
and R. Wong),
2.9: Difference Equations
 papers 26, 33 cited in: G. Mastroianni and G. Milovanovic,
Interpolation processes:
Basic theory and applications, Springer Monographs in Mathematics,
2008
 paper 20 cited in: C. Kuhen,
Multiple Time Scale Dynamics, Springer Applied
Mathematical Sciences 191, 2014
 papers 4, 6, 14, 20, 29, 49, 58, 64 cited in: S. Bodine and D.A. Lutz,
Asymptotic
Integration of Differential and Difference Equations, Springer Lecture
Notes in Mathematics 2129, 2015
4. Constructivenumerical methods for integral equations and
transforms
(10 papers)
5. Numerical functional analysis (8 papers)
some of my most relevant numerical 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

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
paper in 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
paper in SIAM Review 55, 2013)
 Computing approximate Fekete points by
QR factorizations of
Vandermonde matrices, Comput. Math. Appl. 57 (2009)
(with A. Sommariva); see the
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) (see also this paper)

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
Padua points in Chebfun2 by N. Hale and A. Townsend, July 2014
 Compression of multivariate discrete
measures and
applications, Numer. Funct. Anal. Optim. 36 (2015)
(with A. Sommariva); see the
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
(see
paper)
Research collaboration and coordination experience
 Coordinator of the research group
Multivariate polynomial approximation and applications at the
University of Padova
 Member 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 2 Ph.D.s at the Doctoral School
in Mathematics (Curriculum in Computational Mathematics)
of the University of Padova:
Alvise
Sommariva 1999 on topic 4 (presently associate professor of
numerical analysis at the
University of Padova), and
Marco Caliari 2002 on topic 2 (presently associate professor of
numerical analysis at the
University of Verona), see also The
Mathematics Genealogy
Project
 Coadvisor the Ph.D.
Federico Piazzon (2016, on topic 1)
at the Doctoral School
in Mathematics (Curriculum in Computational Mathematics)
of the University of Padova

Supervisor of 4 postdoc fellowships:
Alvise Sommariva 20002004
on topic 4,
Angeles
Martinez 20052006 on topic 2 (presently lecturer of numerical
analysis at the University of Padova),
Marco Caliari 20062007 on topic 2 and
Federico Piazzon 20172018 on topic 1
 Supervisor of 10 "laurea" theses
for the degrees in Mathematics (former 4 years and present
3+2 years curricula) 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, grant: 35 kEuros,
components: 8)
 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, grant: 28 kEuros, components: 4)
 Coordinator
of 13 local projects on topics of multivariate approximation
(years 20052017, about 3 kEuros and 3 components per year)
 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, grant: 5 kEuros, components: 5)
 Coresponsible for the funds
of a INdAMGNCS annual project on "Multivariate approximation: theory
and applications"
(JulyDec. 2017, grant: 7.8 kEuros, components: 14)
 Member of the Horizon 2020 ERAPLANET European project:
GEOEssential (Essential Variables workflows for
resource efficiency and environmental management;
local coordinator: M. Putti)
 Member of the Scientific board (Commissione Scientifica)
for research in Mathematics
and Computer Science, University of Padova (20042005)
 Member of the Council of the Doctoral School in
Mathematics (Curriculum in Computational Mathematics) of the University of
Padova (20052010)
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
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
Approssimazione Multivariata: Teoria ed Applicazioni (AMTA 2017),
Palermo, Italy, Dec. 810 2017
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
 Managing coeditor 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 Committee for the selection of
a postdoc position in numerical analysis at the Dept. of Mathematics
of the University
of Padova (Nov. 2017)
 Referee selected by 35 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 *
International Journal of Computer Mathematics *
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 *
Mathematics and Computers in Simulation *
Mediterranean Journal of Mathematics *
Numerical Algorithms *
Numerical Mathematics: Theory, Methods
and Applications *
Numerische Mathematik *
Rendiconti di Matematica e delle sue Applicazioni *
SIAM Journal on Numerical Analysis *
SIAM Journal on Scientific Computing *
Vietnam Journal of Mathematics
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

"Bivariate interpolation at Xu points"
International Conference  Numerical Analysis: the State
of the Art
(NAC 2005),
Cosenza (Italy) May 2005

"Nearoptimal
interpolation and
quadrature in two variables: the Padua points"
5th European Congress of
Mathematics (5ECM), Amsterdam July 2008

"Approximate Fekete Points"
2nd Dolomites Workshop on Constr.
Approx. and
Applic.
(DWCAA09), Canazei (Italy) Sept. 2009

"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 Tchakaloff Points"
4th Dolomites Workshop on Constr.
Approx. and
Applic.
(DWCAA16), Canazei (Italy) Sept. 2016
Complete list of mathematical publications
published or to appear
2018

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

An elementary approach to polynomial optimization on polynomial
meshes,
J. Math. Fund. Sci. 50 (2018).
2017

A note on total degree polynomial optimization by Chebyshev grids,
Optim. Lett., published online 01 July 2017 (with F. Piazzon).
 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,
In memory of W. Gross. 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).
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).
 A survey on the
LiouvilleGreen (WKB)
approximation for linear difference equations of the second order,
Advances in difference equations (Veszprem, 1995), 567577, Gordon and
Breach, Amsterdam, 1997 (with R. Spigler).
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: a halfcentury of
computational mathematics (Vancouver, BC, 1993), 281285, Proc. Sympos.
Appl. Math., 48, Amer. Math. Soc., Providence, RI, 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,
Asymptotic methods in analysis and combinatorics, 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).
Didactic curriculum
at the University of Padova, from 1991
see also the web page devoted to students:
www.math.unipd.it/~marcov/studenti.html
Teaching (73 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 within the 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) 3 years (2012/13, 2014/15, 2016/17)
 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
 Supervisor of 2 Ph.D. theses 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), and
Marco Caliari 2002 (presently associate professor at the
University of Verona), see also The
Mathematics Genealogy
Project
 Coadvisor of the Ph.D.
Federico Piazzon 2016 (Computational Mathematics, University of
Padova)
 Supervisor of 39 "laurea" theses
for the degrees in Mathematics (former 4 years and present
3+2 years curricula),
most of type
"research thesis" in the area of 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 Council of the Ph.D. program in Computational
Mathematics of the University of Padova (20052010)
 Member of the Board for didactics (Commissione Didattica) of
the Dept. of Mathematics
(20122013)
Complete list of supervised theses for the degrees in Mathematics
(the theses are in Italian unless differently stated)
2014/15
 Positive cubature formulas on normal domains
G. Bergamasco, Tesi di Laurea Triennale
2013/14
 Subperiodic trigonometric hyperinterpolation in
tensorproduct spaces
V. Piciocchi, Tesi di Laurea Magistrale (in English)
 Discrete orthogonal polynomials and hyperinterpolation
over planar regions
M. Zaccaron, Tesi di Laurea Magistrale (in English)
2012/13
 Algebraic cubature on subregions of the sphere
M. Gentile, Tesi di Laurea Magistrale
 Adaptive cubature on the sphere and the torus
L. Mezzalira, Tesi di Laurea Magistrale (as coadvisor)
 Product trigonometric interpolation on spherical sections
A. Cracco, Tesi di Laurea Triennale
 Computing discrete extremal sets on disk sections
A. Passarini, Tesi di Laurea Triennale
2011/12
 Recent results in the theory of polynomial weakly
admissible meshes
F. Piazzon, Tesi di Laurea Magistrale (in English)
 Some results on subperiodic trigonometric approximation
and quadrature
G. Da Fies, Tesi di Laurea Magistrale
 Construction of admissible polynomial meshes on
bidimensional compacts with smooth boundary
V. Piciocchi, Tesi di Laurea Triennale
 Subperiodic trigonometric interpolation and product
interpolation on disk sections
V. Mazzocco, Tesi di Laurea Triennale
2010/11
 Comparison of methods for the numerical integration of
bivariate gaussians over polygons
S. Ballan, Tesi di Laurea Triennale
 Computation of near optimal points for polynomial
interpolation over the triangle
M. Briani, Tesi di Laurea Triennale
2009/10
 Polynomial approximation on weakly admissible meshes of
ball and tetrahedron
G. Orzetti, Tesi di Laurea Magistrale
 A method for convex quadrangulation of a polygon
M. Gentile, Tesi di Laurea Triennale
 Analytic transformations of weakly admissible meshes
F. Piazzon, Tesi di Laurea Triennale
 Algebraic cubature on general domains by the software
system Chebfun
G. Santin, Tesi di Laurea Triennale
2008/09
 A new cubature method over polygons
F. Basaglia, Tesi di Laurea Triennale
2006/07
 A RBF cubature formula for scattered data on domains with
spline boundary
G. Da Fies, Tesi di Laurea Triennale
2005/06
 A RBF cubature formula for scattered data on circular
sectors
A. Punzi, Tesi di Laurea Triennale
2003/04
 Efficient implementation of the Fast Gauss Tranform on
grids
E. Caniato, Tesi di Laurea Quadriennale
2001/02
 Efficient implementation of exponential integrators for 2D
and 3D advectiondiffusion equations
M. Caliari, Ph.D. thesis in Computational Mathematics (in English)
 Numerical analysis of a polynomial explicit method for
stiff differential systems
C. Casazza, Tesi di Laurea Quadriennale
2000/01
 Bivariate Chebyshev series and approximation of integral
operators
A. Mardegan, Tesi di Laurea Quadriennale
1999/00
 Constructive and numerical analysis for a class of
Hammerstein equations arising in transport theory
A. Sommariva, Ph.D. thesis in Computational Mathematics (in English)
 Acceleration of the multidimensional Fast Gauss Transform
M.T. Aneloni, Tesi di Laurea Quadriennale
 Accelerating the solution of integral equations of the
second kind by Chebyshev compression
A. Martignago, Tesi di Laurea Quadriennale
1998/99
 Computing the exponential operator for large, sparse,
nonsymmetric matrices
M. Caliari, Tesi di Laurea Quadriennale
 Implementation of cosine type methods for 2nd order
differential equations with rapidly oscillating solutions
M. Stander, Tesi di Laurea Quadriennale
1997/98
 Analysis and implementation of a numerical solver for
nonlinear integral equations of transport theory
E. Facchinello, Tesi di Laurea Quadriennale
1996/97
 Polynomial approximation of analytic matrix functions
S. Zamborlin, Tesi di Laurea Quadriennale
 Asymptotic approximation for 2nd order linear difference
equations in Banach algebras
T. Solda`, Tesi di Laurea Quadriennale
 Global error control in the numerical solution of stiff
differential systems
S. Tarraran, Tesi di Laurea Quadriennale
1995/96
 Asymptoticnumerical analysis of 2nd order linear difference
equations with polynomial coefficients
F. Pistellato, Tesi di Laurea Quadriennale
 Numerical computation of the Lerch trascendental function
S. Nizzoli, Tesi di Laurea Quadriennale
1994/95
 Convergence acceleration of power series by asymptotic
summation and extrapolation
S. Dassie`, Tesi di Laurea Quadriennale
 On the numerical integration of analytic functions by
GaussGegenbauer formulas
F. Locatelli, Tesi di Laurea Quadriennale
1992/93
 Some results of discrete asymptoticnumerical analysis
with computational applications
C. Damele, Tesi di Laurea Quadriennale
 A numerical approximation method for a class of
fixedpoint equations
A. Sommariva, Tesi di Laurea Quadriennale