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Marco Vianello: work on Multivariate Interpolation and Hyperinterpolation

online publications and preprints (downloadable pdf), with some conference posters
see also the software section


  1. Stability inequalities for Lebesgue constants via Markov-like inequalities
    draft, with F. Piazzon

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

  3. 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

  4. Numerical hyperinterpolation over nonstandard planar regions
    preprint, with A. Sommariva
    Math. Comput. Simulation 141 (2017), 110--120

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

  6. 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)

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

  8. Polynomial fitting and interpolation on circular sections
    preprint, with A. Sommariva
    Appl. Math. Comput. 258 (2015), 410--424

  9. Multivariate Christoffel functions and hyperinterpolation
    with S. De Marchi and A. Sommariva
    Dolomites Res. Notes Approx. DRNA 7 (2014), 26--33

  10. Polynomial approximation on pyramids, cones and solids of rotation
    with S. De Marchi
    Dolomites Res. Notes Approx. DRNA 6 (2013), 20--26

  11. On the Lebesgue constant of subperiodic trigonometric interpolation
    preprint, with G. Da Fies
    J. Approx. Theory 167 (2013), 59--64

  12. 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

  13. Subperiodic trigonometric interpolation and quadrature
    preprint, with L. Bos
    Appl. Math. Comput. 218 (2012), 10630--10638

  14. Computing Fekete and Lebesgue points: simplex, square, disk
    preprint, with M. Briani and A. Sommariva
    J. Comput. Appl. Math. 236 (2012), 2477--2486

  15. 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

  16. Polynomial interpolation and cubature over polygons
    preprint, with M. Gentile and A. Sommariva
    J. Comput. Appl. Math. 235 (2011), 5232--5239

  17. 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

  18. 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

  19. 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

  20. 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

  21. Approximate Fekete points for weighted polynomial interpolation
    preprint, with A. Sommariva
    Electron. Trans. Numer. Anal. 37 (2010), 1--22

  22. 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

  23. Computing approximate Fekete points by QR factorizations of Vandermonde matrices
    preprint, with A. Sommariva
    Comput. Math. Appl. 57 (2009), 1324--1336

  24. New cubature formulae and hyperinterpolation in three variables
    preprint, with S. De Marchi and Y. Xu
    BIT Numerical Mathematics 49 (2009), 55--73

  25. 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)

  26. Hyperinterpolation in the cube
    preprint, with M. Caliari and S. De Marchi
    Comput. Math. Appl. 55 (2008), 2490--2497

  27. 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

  28. 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

  29. Hyperinterpolation on the square
    preprint, with M. Caliari and S. De Marchi
    J. Comput. Appl. Math. 210 (2007), 78--83

  30. 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

  31. 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

  32. 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

  33. On the Lebesgue constant for the Xu interpolation formula
    preprint, with L. Bos and S. De Marchi
    J. Approx. Theory 141 (2006), 134--141

  34. 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

  35. 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