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Marco Vianello: work on Quadrature, Cubature and Summation

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


  1. Quadrature-based polynomial optimization
    draft - with A. Martinez, F. Piazzon and A. Sommariva
    Optim. Lett., to appear

  2. Numerical quadrature on the intersection of planar disks
    preprint, with A. Sommariva
    FILOMAT 31:13 (2017), 4105--4115

  3. Subperiodic trigonometric subsampling: a numerical approach
    preprint, with A. Sommariva
    Appl. Anal. Discrete Math. 11 (2017), 470--483

  4. 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
    such formulas have been used within the parallel multiphysics finite-element research code BACI
    developed at the Institute for Computational Mechanics, TUM Muenchen


  5. Caratheodory-Tchakaloff Subsampling
    with F. Piazzon and A. Sommariva
    Dolomites Res. Notes Approx. DRNA 10 (2017), 5--14
    poster presented at the II Joint Meeting Spain-Brazil in Mathematics (Cadiz, December 11-14 2018)

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

  8. Product Gaussian quadrature on circular lunes
    preprint, with G. Da Fies
    Numer. Math. Theory Methods Appl. 7 (2014), 251--264

  9. Algebraic cubature by linear blending of elliptical arcs
    preprint, with G. Da Fies and A. Sommariva
    Appl. Numer. Math. 74 (2013), 49--61

  10. Algebraic cubature on planar lenses and bubbles
    preprint, with G. Da Fies
    Dolomites Res. Notes Approx. DRNA 5 (2012), 7--12

  11. Trigonometric Gaussian quadrature on subintervals of the period
    preprint, with G. Da Fies
    Electron. Trans. Numer. Anal. 39 (2012), 102--112

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

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

  14. An algebraic cubature formula on curvilinear polygons
    preprint, with G. Santin and A. Sommariva
    Appl. Math. Comput. 217 (2011), 10003--10015

  15. 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

  16. Gauss-Green cubature and moment computation over arbitrary geometries
    preprint, with A. Sommariva
    J. Comput. Appl. Math. 231 (2009), 886--896
    the Matlab code has been used in the CFD package SADoRe: Highly Accurate Lagrangian
    Flux Calculation via Algebraic Quadratures on Spline-Approximated Donating Regions

    by Q. Zhang (see paper in SIAM Review 55, 2013)

  17. 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

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

  19. Nontensorial Clenshaw-Curtis cubature
    preprint, with A. Sommariva and R. Zanovello
    Numer. Algorithms 49 (2008), 409--427

  20. Meshless cubature over the disk by Thin-Plate Splines
    preprint, with A. Punzi and A. Sommariva
    J. Comput. Appl. Math. 221 (2008), 430--436

  21. Product Gauss cubature over polygons based on Green's integration formula
    preprint, with A. Sommariva
    BIT Numerical Mathematics 47 (2007), 441--453
    this algorithm has been cited/used in many works on numerical PDEs, see its GoogleScholar page

  22. Meshless cubature by Green's formula
    preprint, with A. Sommariva
    Appl. Math. Comput. 183 (2006), 1098--1107

  23. Numerical cubature on scattered data by radial basis functions
    preprint, with A. Sommariva
    Computing 76 (2006), 295--310

  24. Fast summation of power series with coefficients analytic at infinity
    with A. Sommariva and R. Zanovello
    Numer. Algorithms 27 (2001), 77--87

  25. A new summation method for power series with rational coefficients
    with S. Dassie`and R. Zanovello
    Math. Comp. 69 (2000), 749--756

  26. Asymptotic summation of power series
    preprint, with S. Dassie`and R. Zanovello
    Numer. Math. 80 (1998), 61--73