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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

Multivariate approximation theory, algorithms and applications

Submitted or in progress


Published or to appear

    to appear

  1. An elementary approach to polynomial optimization on polynomial meshes
    draft
    J. Math. Fund. Sci., to appear
  2. Subperiodic Trigonometric Hyperinterpolation
    draft, with G. Da Fies and A. Sommariva
    to appear in: "Festschrift for the 80th Birthday of Ian Sloan" (invited paper), J. Dick, F.Y. Kuo, H. Wozniakowski Eds., Springer, 2018
  3. Subperiodic trigonometric subsampling: a numerical approach
    draft, with A. Sommariva
    Appl. Anal. Discrete Math., to appear

    2017

  4. A note on total degree polynomial optimization by Chebyshev grids
    preprint, with F. Piazzon
    Optim. Lett., published online 01 July 2017
  5. Numerical quadrature on the intersection of planar disks
    preprint, with A. Sommariva
    FILOMAT 31:13 (2017)
  6. Caratheodory-Tchakaloff Least Squares
    preprint, with F. Piazzon and A. Sommariva
    2017 International Conference on Sampling Theory and Applications (SampTA), IEEE Xplore Digital Library, DOI: 10.1109/SAMPTA.2017.8024337
  7. Numerical hyperinterpolation over nonstandard planar regions
    preprint, with A. Sommariva
    Math. Comput. Simulation 141 (2017), 110--120
  8. 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
  9. 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
  10. 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

  11. Polynomial approximation on Lissajous curves in the d-cube
    preprint, with L. Bos and S. De Marchi
    Appl. Numer. Math. 116 (2017), 47--56
  12. 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)

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

    2016

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

    2015

  16. Polynomial Meshes: Computation and Approximation
    preprint, with S. De Marchi, F. Piazzon and A. Sommariva
    Proceeedings of CMMSE 2015, 414--425, ISBN 978-84-617-2230-3, ISSN 2312-0177
  17. Compression of multivariate discrete measures and applications
    preprint, with A. Sommariva
    Numer. Funct. Anal. Optim. 36 (2015), 1198--1223
  18. Polynomial fitting and interpolation on circular sections
    preprint, with A. Sommariva
    Appl. Math. Comput. 258 (2015), 410--424

    2014

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

    2013

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

    2012

  28. 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
  29. Subperiodic trigonometric interpolation and quadrature
    preprint, with L. Bos
    Appl. Math. Comput. 218 (2012), 10630--10638
  30. Trigonometric Gaussian quadrature on subintervals of the period
    preprint, with G. Da Fies
    Electron. Trans. Numer. Anal. 39 (2012), 102--112
  31. Algebraic cubature on planar lenses and bubbles
    with G. Da Fies
    Dolomites Res. Notes Approx. DRNA 5 (2012), 7--12
  32. Computing Fekete and Lebesgue points: simplex, square, disk
    preprint, with M. Briani and A. Sommariva
    J. Comput. Appl. Math. 236 (2012), 2477--2486
  33. Low cardinality admissible meshes on quadrangles, triangles and disks
    preprint, with L. Bos
    Math. Inequal. Appl. 15 (2012), 229--235

    2011

  34. 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
  35. Polynomial interpolation and cubature over polygons
    preprint, with M. Gentile and A. Sommariva
    J. Comput. Appl. Math. 235 (2011), 5232--5239
  36. An algebraic cubature formula on curvilinear polygons
    preprint, with G. Santin and A. Sommariva
    Appl. Math. Comput. 217 (2011), 10003--10015
  37. 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
  38. 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
  39. 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

  40. Analytic transformations of admissible meshes
    preprint, with F. Piazzon
    East J. Approx. 16 (2010), 313--322
  41. 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

  42. 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
  43. Approximate Fekete points for weighted polynomial interpolation
    preprint, with A. Sommariva
    Electron. Trans. Numer. Anal. 37 (2010), 1--22
  44. On simple approximations to simple curves
    with L. Bos
    Dolomites Res. Notes on Approx. DRNA 3 (2010), 1--6

    2009

  45. Gauss-Green cubature and moment computation over arbitrary geometries
    preprint, with A. Sommariva
    J. Comput. Appl. Math. 231 (2009), 886--896
  46. 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
  47. Computing approximate Fekete points by QR factorizations of Vandermonde matrices
    preprint, with A. Sommariva
    Comput. Math. Appl. 57 (2009), 1324--1336
  48. New cubature formulae and hyperinterpolation in three variables
    preprint, with S. De Marchi and Y. Xu
    BIT Numerical Mathematics 49 (2009), 55--73

    2008

  49. 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)
  50. Nontensorial Clenshaw-Curtis cubature
    preprint, with A. Sommariva and R. Zanovello
    Numer. Algorithms 49 (2008), 409--427
  51. Hyperinterpolation in the cube
    preprint, with M. Caliari and S. De Marchi
    Comput. Math. Appl. 55 (2008), 2490--2497
  52. 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
  53. 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

  54. Product Gauss cubature over polygons based on Green's integration formula
    preprint, with A. Sommariva
    BIT Numerical Mathematics 47 (2007), 441--453
  55. 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
  56. Hyperinterpolation on the square
    preprint, with M. Caliari and S. De Marchi
    J. Comput. Appl. Math. 210 (2007), 78--83

    2006

  57. 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
  58. 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

  59. 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
  60. On the Lebesgue constant for the Xu interpolation formula
    preprint, with L. Bos and S. De Marchi
    J. Approx. Theory 141 (2006), 134--141
  61. Meshless cubature by Green's formula
    preprint, with A. Sommariva
    Appl. Math. Comput. 183 (2006), 1098--1107
  62. Numerical cubature on scattered data by radial basis functions
    preprint, with A. Sommariva
    Computing 76 (2006), 295--310
  63. 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

  64. 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
  65. Adaptive bivariate Chebyshev approximation
    preprint, with A. Sommariva and R. Zanovello
    Numer. Algorithms 38 (2005), no. 1-3, 79--94


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