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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

    2024

  1. Polynomial-free unisolvence of polyharmonic splines with odd exponent by random sampling
    arXiv:2401.13322, with A. Sommariva
    Dolomites Res. Notes Approx. (DRNA), to appear
  2. Homogenization of composite materials reinforced with unidirectional fibres with complex curvilinear cross section: a virtual element approach
    AIMS Math. Eng., to appear, with E. Artioli, G. Elefante and A. Sommariva
  3. Qsurf: compressed QMC integration on parametric surfaces
    arXiv:2304.08090, with G. Elefante and A. Sommariva
    J. Approx. Software, to appear
  4. Tchakaloff-like compression of QMC volume and surface integration on the union of balls
    preprint, with G. Elefante and A. Sommariva
    Calcolo, to appear
  5. Numerical cubature on scattered data by adaptive interpolation
    with R. Cavoretto, A. De Rossi, F. Dell'Accio, F. Di Tommaso, N. Siar and A. Sommariva
    J. Comput. Appl. Math., published online 24 January 2024
  6. Chebyshev admissible meshes and Lebesgue constants of complex polynomial projections
    with L. Bialas-Ciez, D. Kenne and A. Sommariva
    J. Comput. Appl. Math. 443 (2024)

    2023

  7. TetraFreeQ: tetrahedra-free quadrature on polyhedral elements
    preprint, with A. Sommariva
    Appl. Numer. Math., published online 11 July 2023
  8. Random sampling and unisolvent interpolation by almost everywhere analytic functions
    preprint, with F. Dell'Accio and A. Sommariva
    Appl. Math. Lett. 145 (2023)
  9. Low-cardinality Positive Interior cubature on NURBS-shaped domains
    preprint, with A. Sommariva
    BIT Numer. Math. 63 (2023)

    2022

  10. 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)
  11. 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)
  12. 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)
  13. inRS: implementing the indicator function of NURBS-shaped planar domains
    preprint, with A. Sommariva
    Appl. Math. Lett. 130 (2022)
  14. Near-optimal polynomial interpolation on spherical triangles
    preprint, with A. Sommariva
    Mediterr. J. Math. 19 (2022)
  15. 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)
  16. 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

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

    2020

  21. 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"
  22. 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
  23. Near G-optimal Tchakaloff designs
    preprint, with L. Bos and F. Piazzon
    Comput. Statistics 35 (2020), 803--819
  24. 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
  25. Compressed cubature over polygons with applications to optical design
    preprint, with B. Bauman and A. Sommariva
    J. Comput. Appl. Math. 370 (2020)
  26. Algebraic cubature on polygonal elements with a circular edge
    preprint, with E. Artioli and A. Sommariva
    Comput. Math. Appl. 79 (2020), 2057--2066

    2019

  27. CaTchDes: Matlab codes for Caratheodory-Tchakaloff Near-Optimal Regression Designs
    with L. Bos
    SoftwareX 10 (2019)
  28. 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
  29. Chebyshev-Dubiner norming webs on starlike polygons
    preprint
    J. Inequal. Spec. Funct. 10-3 (2019), 26--32
  30. Tchakaloff polynomial meshes
    preprint, with L. Bos
    Ann. Polon. Math. 122 (2019), 221--231
  31. Dubiner distance and stability of Lebesgue constants
    preprint
    J. Inequal. Spec. Funct. 10-2 (2019), 49--60
  32. Markov inequalities, Dubiner distance, norming meshes and polynomial optimization on convex bodies
    preprint, with F. Piazzon
    Optim. Lett. 13 (2019), 1325--1343

    2018

  33. 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)
  34. Subperiodic Dubiner distance, norming meshes and trigonometric polynomial optimization
    preprint
    Optim. Lett. 12 (2018), 1659--1667
  35. Discrete norming inequalities on sections of sphere, ball and torus
    preprint, with A. Sommariva
    J. Inequal. Spec. Funct. 9-4 (2018), 113--121
  36. Nearly optimal nested sensors location for polynomial regression on complex geometries
    preprint, with A. Sommariva
    Sampl. Theory Signal Image Process. 17 (2018), 95--101
  37. Global polynomial optimization by norming sets on sphere and torus
    preprint
    Dolomites Res. Notes Approx. DRNA 11 (2018), 10--14
  38. Stability inequalities for Lebesgue constants via Markov-like inequalities
    preprint, with F. Piazzon
    Dolomites Res. Notes Approx. DRNA 11 (2018), 1--9
  39. 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
  40. An elementary approach to polynomial optimization on polynomial meshes
    preprint
    J. Math. Fund. Sci. 50 (2018), 84--91
  41. A note on total degree polynomial optimization by Chebyshev grids
    preprint, with F. Piazzon
    Optim. Lett. 12 (2018), 63--71

    2017

  42. Numerical quadrature on the intersection of planar disks
    preprint, with A. Sommariva
    FILOMAT 31:13 (2017), 4105--4115
  43. Subperiodic trigonometric subsampling: a numerical approach
    preprint, with A. Sommariva
    Appl. Anal. Discrete Math. 11 (2017), 470--483
  44. 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
  45. Numerical hyperinterpolation over nonstandard planar regions
    preprint, with A. Sommariva
    Math. Comput. Simulation 141 (2017), 110--120
  46. 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
  47. 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
  48. 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

  49. Polynomial approximation on Lissajous curves in the d-cube
    preprint, with L. Bos and S. De Marchi
    Appl. Numer. Math. 116 (2017), 47--56
  50. 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)

  51. Trivariate polynomial approximation on Lissajous curves
    preprint, with L. Bos and S. De Marchi
    IMA J. Numer. Anal. 37 (2017), 519--541

    2016

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

    2015

  54. 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
  55. Compression of multivariate discrete measures and applications
    preprint, with A. Sommariva
    Numer. Funct. Anal. Optim. 36 (2015), 1198--1223
  56. Polynomial fitting and interpolation on circular sections
    preprint, with A. Sommariva
    Appl. Math. Comput. 258 (2015), 410--424

    2014

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

    2013

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

    2012

  66. 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
  67. Subperiodic trigonometric interpolation and quadrature
    preprint, with L. Bos
    Appl. Math. Comput. 218 (2012), 10630--10638
  68. Trigonometric Gaussian quadrature on subintervals of the period
    preprint, with G. Da Fies
    Electron. Trans. Numer. Anal. 39 (2012), 102--112
  69. Algebraic cubature on planar lenses and bubbles
    with G. Da Fies
    Dolomites Res. Notes Approx. DRNA 5 (2012), 7--12
  70. Computing Fekete and Lebesgue points: simplex, square, disk
    preprint, with M. Briani and A. Sommariva
    J. Comput. Appl. Math. 236 (2012), 2477--2486
  71. Low cardinality admissible meshes on quadrangles, triangles and disks
    preprint, with L. Bos
    Math. Inequal. Appl. 15 (2012), 229--235

    2011

  72. 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
  73. Polynomial interpolation and cubature over polygons
    preprint, with M. Gentile and A. Sommariva
    J. Comput. Appl. Math. 235 (2011), 5232--5239
  74. An algebraic cubature formula on curvilinear polygons
    preprint, with G. Santin and A. Sommariva
    Appl. Math. Comput. 217 (2011), 10003--10015
  75. 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
  76. 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
  77. 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

  78. Analytic transformations of admissible meshes
    preprint, with F. Piazzon
    East J. Approx. 16 (2010), 313--322
  79. 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

  80. 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
  81. Approximate Fekete points for weighted polynomial interpolation
    preprint, with A. Sommariva
    Electron. Trans. Numer. Anal. 37 (2010), 1--22
  82. On simple approximations to simple curves
    with L. Bos
    Dolomites Res. Notes on Approx. DRNA 3 (2010), 1--6

    2009

  83. Gauss-Green cubature and moment computation over arbitrary geometries
    preprint, with A. Sommariva
    J. Comput. Appl. Math. 231 (2009), 886--896
  84. 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
  85. Computing approximate Fekete points by QR factorizations of Vandermonde matrices
    preprint, with A. Sommariva
    Comput. Math. Appl. 57 (2009), 1324--1336
  86. New cubature formulae and hyperinterpolation in three variables
    preprint, with S. De Marchi and Y. Xu
    BIT Numerical Mathematics 49 (2009), 55--73

    2008

  87. 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)
  88. Nontensorial Clenshaw-Curtis cubature
    preprint, with A. Sommariva and R. Zanovello
    Numer. Algorithms 49 (2008), 409--427
  89. Hyperinterpolation in the cube
    preprint, with M. Caliari and S. De Marchi
    Comput. Math. Appl. 55 (2008), 2490--2497
  90. 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
  91. 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

  92. Product Gauss cubature over polygons based on Green's integration formula
    preprint, with A. Sommariva
    BIT Numerical Mathematics 47 (2007), 441--453
  93. 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
  94. Hyperinterpolation on the square
    preprint, with M. Caliari and S. De Marchi
    J. Comput. Appl. Math. 210 (2007), 78--83

    2006

  95. 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
  96. 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

  97. 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
  98. On the Lebesgue constant for the Xu interpolation formula
    preprint, with L. Bos and S. De Marchi
    J. Approx. Theory 141 (2006), 134--141
  99. Meshless cubature by Green's formula
    preprint, with A. Sommariva
    Appl. Math. Comput. 183 (2006), 1098--1107
  100. Numerical cubature on scattered data by radial basis functions
    preprint, with A. Sommariva
    Computing 76 (2006), 295--310
  101. 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

  102. 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
  103. 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

  1. 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

  2. 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

  3. 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

  4. 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

  5. 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
  6. 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

  7. 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

  8. Efficient computation of the exponential operator for large, sparse, symmetric matrices
    preprint, with L. Bergamaschi
    Numer. Linear Algebra Appl. 7 (2000), 27--45