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Marco Vianello: work on Polynomial Inequalities and Polynomial Optimization

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


  1. Sharp bounds for optimal polynomial meshes
    in preparation, with A. Kroó and F. Piazzon

  2. Subperiodic Dubiner distance, norming meshes and trigonometric polynomial optimization
    draft

  3. An alternative error bound for grid-based polynomial optimization over the simplex
    draft

  4. Global polynomial optimization by norming sets on sphere and torus
    draft

  5. Discrete norming inequalities on sections of sphere, ball and torus
    draft, with A. Sommariva

  6. Mesh-based polynomial optimization on convex bodies
    draft, with F. Piazzon

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

  8. An elementary approach to polynomial optimization on polynomial meshes
    preprint
    J. Math. Fund. Sci. 50 (2018)

  9. A note on total degree polynomial optimization by Chebyshev grids
    preprint, with F. Piazzon
    Optim. Lett., published online 01 July 2017

  10. 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

  11. 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

  12. 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

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

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

  15. 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

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

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

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

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

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

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

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

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

  24. 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

  25. 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

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

  27. 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