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Marco Vianello: publications and preprints since 2000
online publications and preprints (downloadable pdf), with some
conference posters
see also
the software section
publications on Multivariate Approximation Theory
Submitted or in progress
Published or to appear
2025
-
Nonsingularity of unsymmetric Kansa matrices: random collocation by
MultiQuadrics and Inverse MultiQuadrics
arXiv: 2403.18017, with R. Cavoretto, A. De Rossi,
F. Dell'Accio and A. Sommariva
Math. Comput. Simul., minor revision
-
Random sampling and polynomial-free
interpolation by Generalized MultiQuadrics
arXiv:2404.10117, with A. Sommariva
J. Approx. Theory 306 (2025), 106119
2024
-
Evaluating Lebesgue constants by Chebyshev polynomial
meshes on cube, simplex and ball
arXiv:2311.18656,
with L. Bialas-Ciez, D. Kenne and A. Sommariva
Electron. Trans. Numer. Anal. 60 (2024), 428--445
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CPOLYMESH: Matlab and Python codes for
complex polynomial approximation by Chebyshev
admissible meshes
preprint, with D. Kenne and A. Sommariva
JAS - J. Approx. Software 1, 2 (2024)
-
Polynomial-free unisolvence
of polyharmonic
splines with odd exponent by random sampling
arXiv:2401.13322, with A. Sommariva
Dolomites Res. Notes Approx. (DRNA) 17 (2024), 45--47
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Homogenization of composite materials reinforced with unidirectional
fibres with complex curvilinear cross section: a virtual element
approach
preprint, with E. Artioli, G. Elefante and A. Sommariva
AIMS Math. Eng. 6 (2024), 510--535
-
Unisolvence of random Kansa collocation by Thin-Plate Splines for
the Poisson equation
preprint, with F. Dell'Accio and A. Sommariva
Eng. Anal. Bound. Elem. 165 (2024), 105773
-
Qsurf: compressed QMC integration on parametric surfaces
preprint, with G. Elefante and A. Sommariva
JAS - J. Approx. Software 1, 1 (2024)
-
Tchakaloff-like compression of QMC volume and
surface integration on the union of balls
preprint, with G. Elefante and A. Sommariva
Calcolo 61, 46 (2024)
-
A note on polynomial-free unisolvence of polyharmonic
splines at random points
preprint, with L. Bos and A. Sommariva
Appl. Math. Lett. 157 (2024), 109161
-
Numerical cubature on scattered data by
adaptive interpolation
preprint, with R. Cavoretto, A. De Rossi, F. Dell'Accio,
F. Di Tommaso, N. Siar and A. Sommariva
J. Comput. Appl. Math. 444 (2024), 115793
-
TetraFreeQ: tetrahedra-free quadrature on polyhedral elements
preprint, with A. Sommariva
Appl. Numer. Math. 200 (2024), 389--398
-
Chebyshev admissible meshes and Lebesgue constants of complex
polynomial projections
preprint, with L. Bialas-Ciez, D. Kenne and A. Sommariva
J. Comput. Appl. Math. 443 (2024)
2023
-
Random sampling and unisolvent interpolation
by almost everywhere analytic functions
preprint, with F. Dell'Accio and A. Sommariva
Appl. Math. Lett. 145 (2023)
-
Low-cardinality Positive Interior cubature on NURBS-shaped domains
preprint, with A. Sommariva
BIT Numer. Math. 63, 22 (2023)
2022
-
Cubature rules with positive weights on union of disks
preprint, with A. Sommariva
Dolomites Res. Notes Approx. DRNA 15 (2022) (Special Issue for the 60th
of S. De Marchi, 73--81)
-
CQMC: an improved code for low-dimensional Compressed
Quasi-MonteCarlo cubature
preprint, with G. Elefante and A. Sommariva
Dolomites Res. Notes Approx. DRNA 15 (2022)
(Special Issue "Software for Approximation 2022", 92--100)
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DISC: an adaptive numerical Differentiator by local polynomial Interpolation
on SCattered data
preprint, with F. Dell'Accio, F. Di Tommaso and N. Siar
Dolomites Res. Notes Approx. DRNA 15 (2022)
("Special Issue Software for Approximation 2022", 81--91)
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inRS: implementing the indicator function of NURBS-shaped
planar domains
preprint, with A. Sommariva
Appl. Math. Lett. 130 (2022)
-
Near-optimal polynomial interpolation
on spherical triangles
preprint, with A. Sommariva
Mediterr. J. Math. 19 (2022)
-
RBFCUB: a numerical package for near-optimal meshless cubature
on general polygons
preprint, with R. Cavoretto, A. De Rossi and A. Sommariva
Appl. Math. Lett. 125 (2022)
-
Numerical differentiation
on scattered data through multivariate polynomial interpolation
arXiv preprint 2105.09262, with F. Dell'Accio, F. Di Tommaso and N. Siar
BIT Numer. Math. 62 (2022), 773--801
2021
-
RBF moment computation and meshless cubature on general polygonal
regions
preprint, with A. Sommariva
Appl. Math. Comput. 409 (2021)
-
Numerical hyperinterpolation over spherical triangles
preprint, with A. Sommariva
Math. Comput. Simulation 190 (2021), 15--22
-
Near-algebraic Tchakaloff-like quadrature on spherical triangles
preprint, with A. Sommariva
Appl. Math. Lett. 120 (2021)
-
Computing Tchakaloff-like cubature rules on spline curvilinear polygons
preprint, with A. Sommariva
Dolomites Res. Notes Approx. DRNA 14 (2021), 1--11
2020
-
dCATCH: a numerical package for d-variate near G-optimal Tchakaloff regression
via fast NNLS
with M. Dessole and F. Marcuzzi
MDPI-Mathematics 8(7) (2020) - Special Issue "Numerical Methods"
-
Quadrature-based polynomial optimization
preprint, with A. Martinez, F. Piazzon and A. Sommariva
Optim. Lett. 14 (2020), 1027--1036
co-winner of the OPTL Best Paper Awards for 2020
-
Near G-optimal Tchakaloff designs
preprint, with L. Bos and F. Piazzon
Comput. Statistics 35 (2020), 803--819
-
Accelerating the Lawson-Hanson NNLS solver for large-scale
Tchakaloff regression designs
preprint, with M. Dessole and F. Marcuzzi
Dolomites Res. Notes Approx. DRNA 13 (2020), 20--29
-
Compressed cubature over polygons with applications to
optical design
preprint, with B. Bauman and A. Sommariva
J. Comput. Appl. Math. 370 (2020)
-
Algebraic cubature on polygonal elements with a circular edge
preprint, with E. Artioli and A. Sommariva
Comput. Math. Appl. 79 (2020), 2057--2066
2019
-
CaTchDes: Matlab codes for Caratheodory-Tchakaloff Near-Optimal Regression
Designs
with L. Bos
SoftwareX 10 (2019)
-
Near optimal polynomial regression on norming meshes
preprint, with L. Bos and F. Piazzon
Sampling Theory and Applications 2019, IEEE Xplore Digital Library,
DOI: 10.1109/SampTA45681.2019.9030910
-
Chebyshev-Dubiner norming webs
on starlike polygons
preprint
J. Inequal. Spec. Funct. 10-3 (2019), 26--32
-
Tchakaloff polynomial meshes
preprint, with L. Bos
Ann. Polon. Math. 122 (2019), 221--231
-
Dubiner
distance and stability of Lebesgue constants
preprint
J. Inequal. Spec. Funct. 10-2 (2019), 49--60
-
Markov
inequalities, Dubiner
distance, norming meshes and polynomial optimization
on convex bodies
preprint, with F. Piazzon
Optim. Lett. 13 (2019), 1325--1343
2018
-
Near optimal Tchakaloff meshes for compact sets
with Markov exponent 2
preprint
Dolomites Res. Notes Approx. DRNA 11 (2018), 92--96 (Special Issue on Norm
Levenberg's 60th anniversary)
-
Subperiodic Dubiner distance, norming meshes and trigonometric
polynomial optimization
preprint
Optim. Lett. 12 (2018), 1659--1667
-
Discrete norming inequalities on
sections of sphere, ball and torus
preprint, with A. Sommariva
J. Inequal. Spec. Funct. 9-4 (2018), 113--121
-
Nearly optimal nested sensors location for polynomial
regression on
complex geometries
preprint, with A. Sommariva
Sampl. Theory Signal Image Process. 17 (2018), 95--101
-
Global polynomial optimization by norming sets on sphere and torus
preprint
Dolomites Res. Notes Approx. DRNA 11 (2018), 10--14
-
Stability inequalities for Lebesgue constants via Markov-like
inequalities
preprint, with F. Piazzon
Dolomites Res. Notes Approx. DRNA 11 (2018), 1--9
-
Subperiodic
Trigonometric Hyperinterpolation
preprint, with G. Da Fies and A. Sommariva
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. 283--304
-
An
elementary approach to polynomial optimization on polynomial
meshes
preprint
J. Math. Fund. Sci. 50 (2018), 84--91
-
A note on total degree polynomial optimization by Chebyshev grids
preprint, with F. Piazzon
Optim. Lett. 12 (2018), 63--71
2017
- Numerical
quadrature on the intersection of planar disks
preprint, with A. Sommariva
FILOMAT 31:13 (2017), 4105--4115
-
Subperiodic
trigonometric
subsampling: a numerical approach
preprint, with A. Sommariva
Appl. Anal. Discrete Math. 11 (2017), 470--483
-
Caratheodory-Tchakaloff Least Squares
preprint, with F. Piazzon and A. Sommariva
Sampling Theory and Applications 2017, IEEE Xplore Digital Library, DOI:
10.1109/SAMPTA.2017.8024337
-
Numerical hyperinterpolation over nonstandard planar regions
preprint, with A. Sommariva
Math. Comput. Simulation 141 (2017), 110--120
-
On the use of compressed polyhedral quadrature formulas in embedded
interface
methods
preprint, with Y. Sudhakar, A. Sommariva and W.A. Wall
SIAM J. Sci. Comput. 39 (2017), B571-B587
-
Optimal
polynomial meshes and
Caratheodory-Tchakaloff submeshes
on the sphere
with P. Leopardi and A. Sommariva
Dolomites Res. Notes Approx. DRNA 10 (2017), 18--24
-
Caratheodory-Tchakaloff
Subsampling
with F. Piazzon and A. Sommariva
Dolomites Res. Notes Approx. DRNA 10 (2017), 5--14
poster presented
at DWCAA16, Canazei (Italy), 2016
-
Polynomial approximation on Lissajous curves in the d-cube
preprint, with L. Bos and S. De Marchi
Appl. Numer. Math. 116 (2017), 47--56
- Polynomial
approximation and quadrature
on geographic rectangles
preprint, with M. Gentile and A. Sommariva
Appl. Math. Comput. 297 (2017), 159--179
poster
presented at
SIAM GeoSciences 2013, Padova (Italy)
- Trivariate
polynomial approximation on Lissajous curves
preprint, with L. Bos and S. De Marchi
IMA J. Numer. Anal. 37 (2017), 519--541
2016
-
Jacobi norming meshes
preprint, with F. Piazzon
Math. Inequal. Appl. 19 (2016), 1089--1095
- Compressed
sampling
inequalities by Tchakaloff's theorem
preprint
Math. Inequal. Appl. 19 (2016), 395--400
2015
- Polynomial
Meshes: Computation and Approximation
preprint, with S. De Marchi, F. Piazzon and A. Sommariva
Proceedings of CMMSE 2015, 414--425, ISBN 978-84-617-2230-3, ISSN
2312-0177
- Compression
of multivariate discrete
measures and
applications
preprint, with A. Sommariva
Numer. Funct. Anal. Optim. 36 (2015), 1198--1223
- Polynomial
fitting and interpolation on
circular sections
preprint, with A. Sommariva
Appl. Math. Comput. 258 (2015), 410--424
2014
- Multivariate
Christoffel functions and
hyperinterpolation
with S. De Marchi and A. Sommariva
Dolomites Res. Notes Approx. DRNA 7 (2014), 26--33
- Product
Gaussian quadrature on circular
lunes
preprint, with G. Da Fies
Numer. Math. Theory Methods Appl. 7 (2014), 251--264
- Constructing
optimal polynomial meshes
on planar starlike domains
with F. Piazzon
Dolomites Res. Notes Approx. DRNA 7 (2014), 22--25
- Norming
meshes by Bernstein-like
inequalities
preprint
Math. Inequal. Appl. 17 (2014), 929--936
- Sub-optimal
polynomial meshes
on planar Lipschitz domains
preprint, with F. Piazzon
Numer. Funct. Anal. Optim. 35 (2014), 1467--1475
2013
- Algebraic
cubature by linear blending of
elliptical arcs
preprint, with G. Da Fies and A. Sommariva
Appl. Numer. Math. 74 (2013), 49--61
- Polynomial
approximation on pyramids, cones
and solids of
rotation
with S. De Marchi
Dolomites Res. Notes Approx. DRNA 6 (2013), 20--26
-
Small perturbations of polynomial meshes
preprint, with F. Piazzon
Appl. Anal. 92 (2013), 1063--1073
-
On the Lebesgue
constant of subperiodic
trigonometric
interpolation
preprint, with G. Da Fies
J. Approx. Theory 167 (2013), 59--64
2012
-
On the
generation of symmetric
Lebesgue-like points in the triangle
preprint, with F. Rapetti and A. Sommariva
J. Comput. Appl. Math. 236 (2012), 4925--4932
-
Subperiodic trigonometric interpolation and quadrature
preprint, with L. Bos
Appl. Math. Comput. 218 (2012), 10630--10638
-
Trigonometric Gaussian quadrature on subintervals of the
period
preprint, with G. Da Fies
Electron. Trans. Numer. Anal. 39 (2012), 102--112
-
Algebraic cubature on planar lenses and bubbles
with G. Da Fies
Dolomites Res. Notes Approx. DRNA 5 (2012), 7--12
-
Computing Fekete and Lebesgue points: simplex, square, disk
preprint, with M. Briani and A. Sommariva
J. Comput. Appl. Math. 236 (2012), 2477--2486
-
Low cardinality admissible meshes on quadrangles, triangles and
disks
preprint, with L. Bos
Math. Inequal. Appl. 15 (2012), 229--235
2011
-
On Multivariate Newton Interpolation at Discrete Leja
Points
with L. Bos, S. De Marchi and A. Sommariva
Dolomites Res. Notes Approx. DRNA 4 (2011), 15--20
-
Polynomial interpolation and cubature over polygons
preprint, with M. Gentile and A. Sommariva
J. Comput. Appl. Math. 235 (2011), 5232--5239
-
An algebraic cubature formula on curvilinear polygons
preprint, with G. Santin and A. Sommariva
Appl. Math. Comput. 217 (2011), 10003--10015
-
Geometric Weakly Admissible Meshes, Discrete Least Squares
Approximations and Approximate Fekete Points
preprint, with L. Bos, J.P. Calvi, N. Levenberg and A.
Sommariva
Math. Comp. 80 (2011), 1601--1621
-
Padua2DM: fast interpolation and cubature at the Padua points in
Matlab/Octave
preprint, with M. Caliari, S. De Marchi and A.
Sommariva
Numer. Algorithms 56 (2011), 45--60
-
Weakly Admissible Meshes and Discrete Extremal Sets
preprint, with L. Bos, S. De Marchi and A. Sommariva
Numer. Math. Theory Methods Appl. 4 (2011), 1--12
2010
-
Analytic transformations of admissible meshes
preprint, with F. Piazzon
East J. Approx. 16 (2010), 313--322
-
Computing multivariate Fekete and Leja points by numerical linear
algebra
preprint, with L. Bos, S. De Marchi and A. Sommariva
SIAM J. Numer. Anal. 48 (2010), 1984--1999
poster presented at
ICIAM 2011, Vancouver
-
Least-squares polynomial approximation on weakly admissible
meshes: disk and triangle
preprint, with L. Bos and A. Sommariva
J. Comput. Appl. Math. 235 (2010), 660--668
-
Approximate Fekete points for weighted polynomial interpolation
preprint, with A. Sommariva
Electron. Trans. Numer. Anal. 37 (2010), 1--22
-
On simple approximations to simple curves
with L. Bos
Dolomites Res. Notes on Approx. DRNA 3 (2010), 1--6
2009
-
Gauss-Green cubature and moment computation over arbitrary
geometries
preprint, with A. Sommariva
J. Comput. Appl. Math. 231 (2009), 886--896
-
A numerical code for fast interpolation and cubature at
the Padua points
preprint, with M. Caliari, S. De Marchi and A. Sommariva
Proceedings of the 9th CMMSE (2009), Vol. I,
218--228
-
Computing approximate Fekete points by QR factorizations of
Vandermonde matrices
preprint, with A. Sommariva
Comput. Math. Appl. 57 (2009), 1324--1336
-
New cubature formulae and hyperinterpolation in three variables
preprint, with S. De Marchi and Y. Xu
BIT Numerical Mathematics 49 (2009), 55--73
2008
-
Algorithm 886: Padua2D: Lagrange Interpolation at Padua Points on
Bivariate
Domains
preprint, with M. Caliari and S. De Marchi
ACM Trans. Math. Software 35-3 (2008)
-
Nontensorial Clenshaw-Curtis cubature
preprint, with A. Sommariva and R. Zanovello
Numer. Algorithms 49 (2008), 409--427
-
Hyperinterpolation in the cube
preprint, with M. Caliari and S. De Marchi
Comput. Math. Appl. 55 (2008), 2490--2497
-
Bivariate Lagrange interpolation at the Padua points:
computational aspects
preprint, with M. Caliari and S. De Marchi
J. Comput. Appl. Math. 221 (2008), 284--292
-
Meshless cubature over the disk by Thin-Plate Splines
preprint, with A. Punzi and A. Sommariva
J. Comput. Appl. Math. 221 (2008), 430--436
2007
-
Product Gauss cubature over polygons based on Green's integration
formula
preprint, with A. Sommariva
BIT Numerical Mathematics 47 (2007), 441--453
-
Bivariate Lagrange interpolation at the Padua points: the
ideal theory approach
preprint, with L. Bos, S. De Marchi and Y. Xu
Numer. Math. 108 (2007), 43--57
-
Hyperinterpolation on the square
preprint, with M. Caliari and S. De Marchi
J. Comput. Appl. Math. 210 (2007), 78--83
2006
-
Hyper2d: a numerical code for
hyperinterpolation on
rectangles
preprint, with M. Caliari, S. De Marchi and R.
Montagna
Appl. Math. Comput. 183 (2006), 1138--1147
-
Bivariate Lagrange interpolation at the Padua points: the
generating curve approach
preprint, with L. Bos, M. Caliari, S. De Marchi and Y. Xu
J. Approx. Theory 143 (2006), 15--25
poster presented at
5ECM, Amsterdam, 2008
-
Bivariate interpolation at Xu points: results, extensions and
applications
preprint, with L. Bos, M. Caliari and S. De Marchi
Electron. Trans. Numer. Anal. 25 (2006), 1--16
-
On the Lebesgue constant for the Xu interpolation formula
preprint, with L. Bos and S. De Marchi
J. Approx. Theory 141 (2006), 134--141
- Meshless cubature by
Green's formula
preprint, with A. Sommariva
Appl. Math. Comput. 183 (2006), 1098--1107
- Numerical
cubature on scattered
data by radial basis
functions
preprint, with A. Sommariva
Computing 76 (2006), 295--310
-
A numerical study of the Xu polynomial interpolation formula
in two variables
preprint, with L. Bos, M. Caliari and S. De Marchi
Computing 76 (2006), 311--324
2005
-
Bivariate polynomial interpolation on the square at new nodal sets
preprint, with M. Caliari and S. De Marchi
Appl. Math. Comput. 165/2 (2005), 261--274
-
Adaptive bivariate Chebyshev approximation
preprint, with A. Sommariva and R. Zanovello
Numer. Algorithms 38 (2005), no. 1-3, 79--94
publications on Exponential Integrators
2009
-
A massively parallel
exponential integrator for advection-diffusion models
preprint, with L. Bergamaschi, M. Caliari and A. Martinez
J. Comput. Appl. Math. 231 (2009), 82--91
2007
- The LEM exponential
integrator for
advection-diffusion-reaction equations
preprint, with L. Bergamaschi and M. Caliari
J. Comput. Appl. Math. 210 (2007), 56--63
2006
-
Comparing Leja and Krylov approximations of large scale
matrix exponentials
preprint, with L. Bergamaschi, M. Caliari and A. Martinez
Springer LNCS vol. 3994, 2006 (Proc. of ICCS 2006, Reading, UK), 685--692
2005
-
A parallel exponential integrator for large-scale discretizations
of advection-diffusion models
preprint, with L. Bergamaschi, M. Caliari and A. Martinez
Springer LNCS vol. 3666, 2005 (Proc. of Euro PVM MPI 2005,
Sorrento,
Italy), 483--492
2004
-
The ReLPM exponential integrator for FE discretizations of
advection-diffusion equations
preprint, with L. Bergamaschi and M. Caliari
Springer LNCS vol. 3039, part IV, 2004 (Proc. of ICCS 2004,
Krakow, Poland),
434--442
- Interpolating
discrete advection-diffusion propagators
at Leja sequences
preprint, with L. Bergamaschi and M. Caliari
J. Comput. Appl. Math. 172 (2004), no. 1, 79--99
2003
-
Efficient approximation of the exponential operator for discrete
2D advection-diffusion problems
preprint, with L. Bergamaschi and M. Caliari
Numer. Linear Algebra Appl. 10 (2003), 271--289
2000
-
Efficient computation of the exponential operator for large,
sparse, symmetric matrices
preprint, with L. Bergamaschi
Numer. Linear Algebra Appl. 7 (2000), 27--45