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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. Lune-based quadrature on vignetted annular pupils with application to the LSST camera
    in preparation, with B. Bauman (LLNL, USA) and A. Sommariva

  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 DWCAA16, Canazei (Italy), 2016

  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

  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