Back to Home Page
Stefano De Marchi: publications and preprints
My Hindex and citations from Google Scholar
Works in progress
Submitted
 On the Convergence of the Rescaled Localized Radial Basis
Function Method
draft (May 2019), with H. Wendland

ShapeDriven Interpolation with Discontinuous Kernels: Error Analysis, Edge Extraction and Applications in MPI
draft (Mar. 2019) with W. Erb, F. Marchetti, E. Perracchione and M. Rossini

Polynomial interpolation via mapped bases without resampling
draft (Feb. 2019) with F. Marchetti, E. Perracchione and D. Poggiali
 A stable meshfree PDE solver for sourcetype flows in porous media
draft (Dec. 2018) with R. Campagna, S. Cuomo, E. Perracchione and G. Severino
 Jumping with Variably Scaled Discontinuos Kernels (VSDK)
draft (Aug. 2018), with F. Marchetti and E. Perracchione.
Accepted/In Press
 On the Lebesgue constant of the trigonometric FloaterHormann rational interpolant at equally spaced nodes
draft (Feb. 2019) with C. Bandiziol, accepted by Dolomites Res. Notes Approx.
 In the footsteps of Copernicus: Padova (Italy) and Uppsala (Sweden)
draft (May 2018) with M. Klimek, to appear in the Irish Math. Soc. Bulletin
 A Kinetic Neural Network Approach for Absolute Quantification and Change Detection in Positron Emission Tomography
draft (Apr. 19), with D. Poggiali and D. Cecchin. To appear in the proceedings of MASCOT2018IMACS Workshop.
2019

Analysis of a new class of rational RBF expansions
draft (Feb. 2018) with M. Buhmann, E. Perracchione, IMA J. Numer. Analysis online first

RBFbased partition of unity method for elliptic PDEs: Adaptivity and stability issues via VSKs
draft (June 2017) with A. Martinez, E. Perracchione and M. Rossini. J. Sci. Comput. 79(1) (2019), pp. 321344
online first
 Mathematics and Oenology: exploring an unlikely pairing. (Mathematics and wine)
with L. Cadeddu and A. Cauli.
in
Handbook of the Mathematics of the Arts and Sciences", pp. 131, doi:10.1007/9783319706580_671, Springer 2019.
Ed. B. Sriraman.

Fast and stable rational RBFbased Partition of Unity interpolation
draft with A. Martinez, E. Perracchione. J. Comput. Appl. Math. 349 (2019), pp. 331343
online version.
2018
 Image Reconstruction from Scattered
Radon Data with Weighted Positive Definite Kernel Functions
draft, with A. Iske and G. Santin, Calcolo 55(2) (2018),
https://doi.org/10.1007/s1009201802476.
 QuasiMonte Carlo integration on manifolds with mapped lowdiscrepancy points and greedy minimal Riesz $s$energy points,
draft, with G. Elefante, Appl. Num. Math. 127(5), pp. 110124 (2018),
online version
 On multivariate MarcinkiewiczZygmund type inequalities
draft (August 2017), with A. Kroó Acta Math. Hungar. 151(1), pp.6989 (2018),
online version .
2017
 Ricci tensors and wine in
Lugo di Romagna and Padova, Italy
draft (Apr. 2017) with G. Andreatta, Math. Intelligencer 39 (3), pp. 5660.
online version .
 Lissajous sampling and spectral filtering in
MPI applications: the reconstruction algorithm for reducing the Gibbs phenomenon
draft (Feb. 2017) with W. Erb and F. Marchetti, Proceedings of SampTA 2017. , pp. 580584.
IEEE Xplore Digital Library DOI: 10.1109/SAMPTA.2017.8024375
 A rescaled method for RBF approximation
draft (Nov. 2016) with A. Idda and G. Santin, Proceedings of "Approximation Theory XV",
Springer Proceedings on Mathematics and Statistics, Vol. 201 (2017), pp.3959.
 Spectral filtering for the reduction of the Gibbs phenomenon of polynomial approximation
methods on Lissajous curves with applications in MPI
with W. Erb and F. Marchetti, Dolomites Res. Notes Approx. 10 (2017), pp. 128137.
 Partition of unity interpolation using stable kernelbased techniques
(draft), with R. Cavoretto et al., Appl. Numer. Math. 116 (2017), pp. 95107,
online.
 Polynomial approximation on Lissajous
curves in the dcube ,
proceeding conference honoring prof. F.
Costabile, with L. Bos and M. Vianello.
Appl. Numer. Math., available online 26 January 2017
here
 Trivariate polynomial approximation on Lissajous curves
with L. Bos and M. Vianello. IMA J. Numer. Analysis (2017) 37, pp. 519541.
2016
 A new quasiMonte Carlo technique based on nonnegative leastsquares and approximate Fekete points
(draft) with C. Bittante and G. Elefante. Numer. Math. TMA. 9(4) (2016), pp. 640663;
doi: 10.4208/nmtma.2016.m1516 .
 Kernelbased Image Reconstruction from Scattered Radon Data
(draft) with A. Iske, A. Sironi. Dolomites Res. Notes on Approx. Vol 9,
special
issue for the workshop "Kernelbased methods and function approximation", pp. 1931.
 Approximating basins of attraction for dynamical systems
via stable radial bases
R. Cavoretto, S. De Marchi, A. De Rossi, E. Perracchione
and G. Santin
AIP Conference Proceedings, 1738, 390003 (2016); doi:10.1063/1.4952177
online
2015
 Fast computation of orthonormal bases for RBF spaces through Krylov spaces methods
(draft, Nov. 2014), with G. Santin, BIT Numerical Math. 55(4) (2015), pp. 949966.
 RBF approximation of large datasets by partition of unity
and local stabilization
(draft, May 2015) with R. Cavoretto et al., Proceedings of CMMSE 2015, Vol. IIIIIIIV, pp. 317326.
 Polynomial Meshes: Computation and Approximation
(draft, May 2015) with F. Piazzon, A. Sommariva and M. Vianello
Proceedings of CMMSE 2015, Vol. IIIIIIIV, pp. 414425.
 A few remarks on "On certain Vandermonde determinants
whose variables separate"
(draft, May 2015) with A. P. de Camargo, Dolomites Res. Notes Approx. 8 (2015), pp. 111.
 Analytical and experimental FWHM of a gamma camera:
theoretical and practical issues ,
(reviewed version, 2015), with D. Cecchin, D, Poggiali, L. Riccardi, P. Turco, F. Bui, PeerJ 3:e722; DOI 10.7717/peerj.722 (2015).
 On the constrained MockChebyshev least squares,
(draft Nov. 2014) with F. Dell'Accio and M. Mazza, J. Comput. Appl. Math. 280 (2015), pp. 94109.
Online version here
2014
 Multivariate Christoffel functions and
hyperinterpolation
draft, with A. Sommariva and M. Vianello, Dolomites Res. Notes Approx. Vol. 7 (2014), pp. 2633.
 Fekete Type Points for Ridge Function Interpolation and Hyperbolic Potential Theory
with L. Bos and N. Levenberg, Publ. Math. Inst. (Beograd), Vol. 110 (2014), pp. 4148.
 Proceedings of the workshop Multivariate Approximation 2013 .
Guest editor of the
Special issue of Dolomites Res. Notes Approx. Vol. 7 (2014).
 On certain multivariate Vandermonde determinants whose variables separate
draft, with K. Usevich, Linear Alg. Appl., Vol. 449 (2014), pp. 1727.
2013
 Polynomial approximation on pyramids, cones and solids of rotation
draft, with M. Vianello, Dolomites Res. Notes Approx, Proceedings DWCAA12, Vol. 6 (2013), pp. 2026
Matlab package for 3dimensional WAMs: 3dWAM
 A new stable basis for radial basis function interpolation
draft, with G. Santin, J. Comp. Appl. Math., Vol. 253 (2013), pp. 113. online
 Bounding the Lebesgue constant of Berrut's rational interpolant
at general nodes
draft, with L. Bos, K. Hormann and J. Sidon, J. Approx. Theory Vol. 169 (2013), pp. 722. most cited of JAT 2018
2012
 Polynomial approximation and cubature
at approximate Fekete and Leja points of the cylinder
draft, with M. Marchioro and A. Sommariva, Appl. Math. Comput.
Vol. 218(21), pp. 1061710629
 On the Lebesgue constant of
barycentric rational interpolation at equidistant nodes
draft, with L. Bos, K. Hormann and G. Klein, Numer. Math. 121(3) 2012, 461471
 A mathematical view of matching food and
wine
draft, Int. J. Contemp. Math. Sciences (7) 2012, no. 33, 1639  1652
Matlab files.

Barycentric rational interpolation at quasiequidistant nodes
draft, with K. Hormann and G. Klein, Dolomites Research Notes Approx, Vol 5, 2012, pp. 16
2011
 On the WhittakerShannon sampling
by means of Berrut's rational interpolant and its extension by Floater and Hormann
draft, with L. Bos, East J. Approx. 17(3) (2011), pp. 267284
 On optimal points for interpolation by univariate exponential functions
draft, with L. Bos, Dolomites Research Notes on Approx. (DRNA), Vol. 4 (2011), pp. 812.

Dolomites Research Notes on Approximation (DRNA), Vol. 4, Special Issue for the
Proceedings of Robert Schaback's 65th birthday, pp. 63,
Guest editors: M. Buhmann, S. De Marchi and G. PlonkaHock.
 On Multivariate Newton Interpolation
at Discrete Leja Points
draft, with L. Bos, A. Sommariva and M. Vianello, Dolomites Res. Notes Approx, Vol. 4 (Proceedings of Robert Schaback's 65th birthday), pp. 1520.
 On the Lebesgue constant of Berrut's rational interpolant
at equidistant nodes
draft, with L. Bos and K. Hormann, J. Comput. Appl. Math. 236 (2011), pp. 504510.
 Preface
with C. Brezinki, J. M. Carnicer, A. Iske, M. RedivoZaglia, S. Seatzu, E. Venturino and M. Vianello
Calcolo 48 (2011), pp. 13

Padua2DM: fast interpolation and cubature at the Padua points in
Matlab/Octave
draft, with M. Caliari, A.
Sommariva and M. Vianello, Numer. Algorithms Vol. 56(1), 2011, pp. 4560,
online

Weakly Admissible Meshes
and Discrete Extremal Sets
draft, with L. Bos, A. Sommariva and M. Vianello
Numer. Math. Theor. Meth. Appl. Vol. 4(1), 2011, pp. 112
2010

Computing multivariate Fekete
and Leja points by numerical linear algebra
draft, with L. Bos, A. Sommariva and M. Vianello
SIAM J. Num. Anal. Vol. 48(5), 2010, pp. 19841999.
Available on line: here
 Special Issue of Numer. Algorithms Vol 55, 23, Preface pp. 141143 (2010)
with J. M. Carnicer, M. Redivo Zaglia, E. Venturino and M. Vianello
"Second Dolomites Workshop on Constructive Approximation and Applications (DWCAA09)".

Stability of KernelBased Interpolation
draft, with R. Schaback
Adv. Comput. Math. Vol. 32(2), 2010, p. 155161
available on
line.
Examples and more
These are the examples and the figures illustrating the results
of the paper Stability of KernelBased Interpolation.
2009

Nonstandard kernels and their Applications
draft, with R. Schaback.
DRNA (Dolomites Research Notes on Approximations) Vol. 2, 2009, pp. 1643.
Matlab and Maple files.

On the Vandermonde Determinant of Padualike Points
draft, with L. Bos and S. Waldron
an Open Problem for
DRNA (Dolomites Research Notes on Approximation), Vol. 2, 2009, pp. 115.

Geometric greedy and greedy points for RBF
interpolation
Draft. Proceedings of the 9th CMMSE (Gijon, Spain, July 2009), Vol. II, pp. 381392
Editors: P. Alonso, S. Oharu, E. Venturino and B. A. Wade.

A numerical code for fast interpolation and cubature at the Padua points
draft, with M. Caliari, A. Sommariva and M. Vianello.
Proceedings of the 9th CMMSE (Gijon, Spain, July 2009), Vol. I, p. 218228.
Editors: P. Alonso, S. Oharu, E. Venturino and B. A. Wade.

New cubature formulae and hyperinterpolation in three variables
draft, with M. Vianello and Y. Xu.
BIT Numerical Mathematics, Vol. 49(1) 2009, 5573.
on line
2008

Bivariate Lagrange interpolation at the Padua points:
computational aspects
draft, with M. Caliari and M. Vianello
J. Comput. Appl. Math., Vol. 221 2008, 284292.

Algorithm 886: Padua2D: Lagrange Interpolation at Padua Points on
Bivariate
Domains
draft, with M. Caliari and M. Vianello
ACM Trans. Math. Software, Vol. 35(3), Article 21, 11 pages, 2008.

Hyperinterpolation in the cube
draft, with M. Caliari and M. Vianello
Comput. Math. Appl., Vol. 55(11) 2008, 24902497.

Univariate Radial Basis Functions with Compact Support Cardinal
Functions
draft, with L. Bos
East J. Approx., Vol. 14(1) 2008, 6980.
2007

Bivariate Lagrange interpolation at the Padua points: the
ideal theory approach
preprint, with L. Bos, M. Vianello and Y. Xu
Numer. Math., 108(1) (2007), 4357.

Hyperinterpolation on the square
preprint, with M. Caliari and M. Vianello
J. Comput. Appl. Math. 210(12) (2007), 7883

GuestEditor Preface
with M. RedivoZaglia and M. Vianello
Numer. Algorithms 45 (14) (2007), 19,
"1st Dolomites Workshop on Constructive Approximation and Applications (DWCAA06)"

Mathematics and wine
preprint
Appl. Math. Comput. 192 (2007), 180190
Some comments to the paper bt written by Nicoló Regazzoni in
bargiornale.it, 22 October 2007
2006

Polynomials arising in factoring generalized Vandermonde determinants III
:computation of their roots
preprint, with M. Morandi Cecchi
Neural, Parallel and
Scientific Computations 14 (2006), 2538

Parametric method for global optimization in Hilbert Spaces
preprint, with I. Raykov
J. of Optim.
Theory and Applications (JOTA) 130(3) (2006), 411430

Hyper2d: a numerical code for
hyperinterpolation on
rectangles
preprint, with M. Caliari, R.
Montagna and M. Vianello
Appl. Math. Comput. 183 (2006), 11381147

Bivariate Lagrange interpolation at the Padua points: the
generating curve approach
preprint, with L. Bos, M. Caliari, M. Vianello and Y. Xu
J. Approx. Theory 143 (2006), 1525
classified in the TOP 25 Hottest Articles of JAT, Oct.Dec. 2006

Bivariate interpolation at Xu points: results, extensions and
applications
preprint, with L. Bos, M. Caliari and M. Vianello
Electron. Trans. Numer. Anal. 25 (2006), 116

On the Lebesgue constant for the Xu interpolation formula
preprint, with L. Bos and M. Vianello
J. Approx. Theory 141 (2006), 134141
classified in the TOP 25 Hottest Articles of JAT, JulySept. 2006

A numerical study of the Xu polynomial interpolation formula
in two variables
preprint, with L. Bos, M. Caliari and M. Vianello
Computing 76(34)(2006), 311324
2005

Bivariate polynomial interpolation on the square at new nodal sets
preprint, with M. Caliari and M. Vianello
Appl. Math. Comput. 165(2) (2005), 261274

NearOptimal
Dataindependent Point Locations for Radial Basis
Function Interpolation
preprint, with R. Schaback and H. Wendland
Adv. Comput. Math. 23(3) (2005), 317330

Sets of NearOptimal Points for Interpolation on the Square
preprint
APPLIED AND INDUSTRIAL MATHEMATICS IN ITALY
Proceedings of the 7th Conference, Venice (Italy), 20  24 September 2004
Ed. M. Primicerio et al., pp. 4555 (2005)
2004

On Leja sequences: some results and applications
preprint
Appl. Math. Comput. 152(3) (2004), 621647

On blossoming in integer Müntz spaces
preprint, with C. Roveredo
Int. Math. J. 5(1) (2004), 6166
2003

On optimal center locations for radial basis
interpolation: computational aspects
preprint
Rend. Sem. Mat. Torino, 61(3) (2003), 343358

Fast evaluation of
discrete integral operators by Chebyshev and Leja polynomial approximation
preprint, with M. Vianello
"Constructive Function Theory", Varna 2002 (B. Bojanov,
Ed.),pp. 347353, DARBA Sofia 2003.
2002

On
the limit under scaling of
polynomial Lagrange interpolation on analytic manifolds
preprint, with L. Bos
Rend. Circolo Matematico Palermo, Serie II, Suppl. 68 (2002), 303314

An interpolant defined by subdivision and the analysis of the error
preprint, with A. Ligun, A. Schumeiko and S. Timchenko
J. Comput. Appl. Math. 145(1) (2002), 7188

Polynomials arising in factoring generalized
Vandermonde determinants II: a condition for monicity
preprint
Appl. Math. Lett. 15(5) (2002), 627632
2001

Approximating the approximant : a numerical
code for the polynomial compression of discrete integral operators
preprint, with M. Vianello
Numer. Algorithms 28 (2001), 101116

Polynomials arising in factoring generalized
Vandermonde determinants: an algorithm for computing their coefficients
preprint
Math. Comput. Modelling 34 (2001), 271281
19932000

Fekete points for bivariate polynomials
restricted to y=x^{m}
preprint, with L. Bos
East J. Approx. 6(2) (2000), 189200

On
computing the factors of generalized
Vandermonde determinants
In Recent Advances in Applied and Theoretical Mathematics
Math. Comput. Sci. Eng., World Sci. Eng. Soc. Press, (2000), 140144

Limiting values under scaling of the Lebesgue function for
polynomial interpolation on spheres.
preprint, with L. Bos
J. Approx. Theory 96(2) (1999), 366377

A Package for Representing C^{1}Interpolating
Surfaces: Application to the Lagoon of Venice's Bed
preprint, with D. Fasoli and M. Morandi Cecchi
Numer. Algorithms 20(23) (1999), 197215

On
computing derivatives for C^{1}
interpolating schemes: an optimization
preprint
Computing 60 (1)(1998), 2953

Peano's kernel theorem for vectorvalued functions: a weak version in normed spaces
preprint, with M. Vianello
Numer. Func. Anal. Optim. 18 (1&2)(1997), 6574

Peano's kernel theorem for vectorvalued functions and some applications
preprint, with M. Vianello
Numer. Func. Anal. Optim. 17 (1&2)(1996), 5764

Reference Functional and Characteristic
Space for Lagrange and Bernstein Operators
Abstract, with M. Morandi Cecchi
Approx. Theory Appl. (N.S.) 11(4) (1995), 614

The polynomial approximation in the
finite element method
preprint, with M. Morandi Cecchi
J. Comput. Appl. Math. 57 (12) (1995), 99114

Can Irregular Subdvisions Preserve Convexity ?
abstract, with Morandi Cecchi
Approximation Theory, wavelets and applications,
NATO Adv. Sci. Inst. Ser. C Math. Phys.Sci. 454
Kluwer Acad. Publi. (1995), 325334
 Splitting functions and numerical analysis of WRtype methods for evolutionary and stationary problems
with M. Vianello and R. Zanovello
In Mathematics of Computation 19431993: a half century of computational mathematics
Proc. Sympos. Appl. Math. (48) (1994), 281285
 Fractal interpolation functions for a class of finite
elements
with M. Morandi Cecchi
In Wavelets, images and suface fitting
A. K. Peters, Wellesley (1994), 189196
 Inverse kinematics robot calibration by spline functions.
with F. Agrilli and A. Doria
Appl. Math. Modelling 17(9) (1993)
Relevant technical reports

Stability constants for kernelbased interpolation processes
with R. Schaback
University of Verona, RR 59/2008.

A study on Premixed Laminar Flames
with G. Argentini, M. Caliari and S. Zuccher
University of Verona, RR 46/2006.

Generalized Vandermonde determinants, Toeplitz matrices and Schur functions
Universitaet Dortmund, Ergebnisberichte Angewandte Mathematik, 176/1999.

LABSUP: a LAboratory
for Bivariate C^{1} SUrfaces and Patches
with Damiano Fasoli and Maria Morandi Cecchi
University of Padova, RI 9/1996.

The Dyadic Iterative Interpolation Method and Some Extensions
with M. Morandi Cecchi
University of Padova, RI 10/1994
Translation

On the systems of Feketepoints of an arc of circumference
preprint, by B. Germanski. Tranlation done with L. Brutman.
East J. Approx. 8(4), 2002, 511524
Books

Exercises of Numerical Calculus
I Edizione 2017, pp. 122, ISBN: 9788898648535
Editrice La DottaBologna

Meshfree Approximation for MultiAsset European and American Option Problems
I Edizione 2012, pp. 92, ISBN: 9788854851511
Editrice AracneRoma

Appunti di Calcolo Numerico (in Italian)
II Edizione 2016, pp. 260, ISBN: 9788874889396
Editrice EsculapioBologna

Funzioni splines univariate
Editrice Universitaria Udinese FORUM (2001)
For copies you must contact the publisher at the following
address: Via Larga, 38  33100 Udine, tel. 0432 26001.

Approssimazione e Interpolazione su "Simplices": Caratterizzazioni,
Metodi ed Estensioni
Ph.D. thesis (in Italian, 1994).
The thesis is available at the Florence national library
here
Software

The LABSUP
package at the Netlib

Bivariate polynomial interpolation software and miscellanea
Miscellanea Mathematics
 Il paradosso francese
in MaddMaths, MAtematica Divulgazione Didattica, 21 Dec. 2011.
 Simai per la divulgazione, l'angolo arguto: Il paradosso francese
 From Matematicamente of Mathesis  Verona:
nr. 113
nr. 118
Miscellanea: articles in local magazines, weekly, blogs, ejournals (in Italian)
 La Difesa del Popolo (Oct. 2012):
AC: la scelta reliogiosa é restrittiva? Intervista.
 Toniolo Ricerca (Nov. 2011):
Multiculturalitè e patto costituzionale nei 150 anni dell'unità d'Italia .
 Lettera Diocesana 2011/17:
Openfield 2011: Editoriale
 La Difesa del Popolo (Ago. 2011):
Openfield 2011: Multiculturalit?? e patto costituzionale. Intervista.
 La Difesa del Popolo (Mag. 2011): Laici e impegno sociopolitico
 Toniolo Ricerca (Mag. 2011): Univeneto, si parte!.
 La Difesa del Popolo (Apr. 2011): Quando le ferite
non minano la dignità
 Toniolo Ricerca (Dic. 2010):
Universo Università.
 Blog della Strada del Vino dei Colli Euganei Gocce di matematica??serata con i vini Severi
 La Difesa del Popolo (Mar. 2011): 17 marzo: una festa poco sentita
 La Difesa del Popolo (Feb. 2010): Cristiani in politica
 La Difesa del Popolo (Nov. 2009): Riforma Università
 From Blog
Andrea Scanzi  Feb. 2008
 La
Piazza del Conselvano  Feb. 2008
 From the
Sommelier Veneto 1/08
 From the
Sommelier Veneto 1/07