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Marco Vianello: work on Polynomial Inequalities and Norming Meshes

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


  1. Near-optimal polynomial interpolation on spherical triangles
    preprint, with A. Sommariva
    Mediterr. J. Math. 19 (2022)

  2. Near G-optimal Tchakaloff designs
    preprint, with L. Bos and F. Piazzon
    Comput. Statistics 35 (2020), 803--819

  3. 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

  4. Chebyshev-Dubiner norming webs on starlike polygons
    preprint
    J. Inequal. Spec. Funct. 10-3 (2019), 26--32

  5. Tchakaloff polynomial meshes
    preprint, with L. Bos
    Ann. Polon. Math. 122 (2019), 221--231

  6. Dubiner distance and stability of Lebesgue constants
    preprint
    J. Inequal. Spec. Funct. 10-2 (2019), 49--60

  7. Markov inequalities, Dubiner distance, norming meshes and polynomial optimization on convex bodies
    preprint, with F. Piazzon
    Optim. Lett. 13 (2019), 1325--1343

  8. 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 birthday)

  9. Subperiodic Dubiner distance, norming meshes and trigonometric polynomial optimization
    preprint
    Optim. Lett. 12 (2018), 1659--1667

  10. Discrete norming inequalities on sections of sphere, ball and torus
    preprint, with A. Sommariva
    J. Inequal. Spec. Funct. 9-2 (2018), 113--121

  11. Global polynomial optimization by norming sets on sphere and torus
    preprint
    Dolomites Res. Notes Approx. DRNA 11 (2018), 10--14

  12. Stability inequalities for Lebesgue constants via Markov-like inequalities
    preprint, with F. Piazzon
    Dolomites Res. Notes Approx. DRNA 11 (2018), 1--9

  13. An elementary approach to polynomial optimization on polynomial meshes
    preprint
    J. Math. Fund. Sci. 50 (2018), 84--91

  14. A note on total degree polynomial optimization by Chebyshev grids
    preprint, with F. Piazzon
    Optim. Lett. 12 (2018), 63--71

  15. 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

  16. Optimal polynomial meshes and Caratheodory-Tchakaloff submeshes on the sphere
    preprint, with P. Leopardi and A. Sommariva
    Dolomites Res. Notes Approx. DRNA 10 (2017), 18--24

  17. 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

  18. Jacobi norming meshes
    preprint, with F. Piazzon
    Math. Inequal. Appl. 19 (2016), 1089--1095

  19. Compressed sampling inequalities by Tchakaloff's theorem
    preprint
    Math. Inequal. Appl. 19 (2016), 395--400

  20. 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

  21. Compression of multivariate discrete measures and applications
    preprint, with A. Sommariva
    Numer. Funct. Anal. Optim. 36 (2015), 1198--1223

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

  23. Constructing optimal polynomial meshes on planar starlike domains
    with F. Piazzon
    Dolomites Res. Notes Approx. DRNA 7 (2014), 22--25

  24. Norming meshes by Bernstein-like inequalities
    preprint
    Math. Inequal. Appl. 17 (2014), 929--936

  25. Sub-optimal polynomial meshes on planar Lipschitz domains
    preprint, with F. Piazzon
    Numer. Funct. Anal. Optim. 35 (2014), 1467--1475

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

  27. Small perturbations of polynomial meshes
    preprint, with F. Piazzon
    Appl. Anal. 92 (2013), 1063--1073

  28. Low cardinality admissible meshes on quadrangles, triangles and disks
    preprint, with L. Bos
    Math. Inequal. Appl. 15 (2012), 229--235

  29. 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

  30. 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

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

  32. 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