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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

Numerical cubature on polygonal elements with one curved side
in preparation, with E. Artioli and A. Sommariva

Quadraturebased polynomial optimization
draft  with A. Martinez, F. Piazzon and A. Sommariva
 Numerical
quadrature on the intersection of planar disks
preprint, with A. Sommariva
FILOMAT 31:13 (2017), 41054115

Subperiodic
trigonometric
subsampling: a numerical approach
preprint, with A. Sommariva
Appl. Anal. Discrete Math. 11 (2017), 470483

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), B571B587
such formulas have been used within the
parallel multiphysics
finiteelement research
code BACI
developed at
the
Institute for Computational Mechanics, TUM Muenchen

CaratheodoryTchakaloff
Subsampling
with F. Piazzon and A. Sommariva
Dolomites Res. Notes Approx. DRNA 10 (2017), 514
poster presented
at DWCAA16, Canazei (Italy), 2016
 Polynomial approximation and quadrature
on geographic rectangles
preprint, with M. Gentile and A. Sommariva
Appl. Math. Comput. 297 (2017), 159179
poster
presented at
SIAM GeoSciences 2013, Padova (Italy)
 Compression of multivariate discrete
measures and
applications
preprint, with A. Sommariva
Numer. Funct. Anal. Optim. 36 (2015), 11981223
 Product Gaussian quadrature on circular
lunes
preprint, with G. Da Fies
Numer. Math. Theory Methods Appl. 7 (2014), 251264
 Algebraic cubature by linear blending of
elliptical arcs
preprint, with G. Da Fies and A. Sommariva
Appl. Numer. Math. 74 (2013), 4961
 Algebraic
cubature on planar lenses
and bubbles
preprint, with G. Da Fies
Dolomites Res. Notes Approx. DRNA 5 (2012), 712

Trigonometric Gaussian quadrature on subintervals of the
period
preprint, with G. Da Fies
Electron. Trans. Numer. Anal. 39 (2012), 102112

Subperiodic trigonometric interpolation and quadrature
preprint, with L. Bos
Appl. Math. Comput. 218 (2012), 1063010638

Polynomial interpolation and cubature over polygons
preprint, with M. Gentile and A. Sommariva
J. Comput. Appl. Math. 235 (2011), 52325239

An algebraic cubature formula on curvilinear polygons
preprint, with G. Santin and A. Sommariva
Appl. Math. Comput. 217 (2011), 1000310015

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), 4560

GaussGreen cubature and moment computation over arbitrary
geometries
preprint, with A. Sommariva
J. Comput. Appl. Math. 231 (2009), 886896
the Matlab code has been used in the
CFD package SADoRe: Highly
Accurate Lagrangian
Flux Calculation
via Algebraic
Quadratures
on SplineApproximated Donating Regions
by Q. Zhang (see
paper in SIAM Review 55, 2013)

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,
218228

New cubature formulae and hyperinterpolation in three variables
preprint, with S. De Marchi and Y. Xu
BIT Numerical Mathematics 49 (2009), 5573

Nontensorial ClenshawCurtis cubature
preprint, with A. Sommariva and R. Zanovello
Numer. Algorithms 49 (2008), 409427

Meshless cubature over the disk by ThinPlate Splines
preprint, with A. Punzi and A. Sommariva
J. Comput. Appl. Math. 221 (2008), 430436

Product Gauss cubature over polygons based on Green's integration
formula
preprint, with A. Sommariva
BIT Numerical Mathematics 47 (2007), 441453
this algorithm has been cited/used in many works on numerical PDEs,
see its
GoogleScholar page
 Meshless cubature by Green's formula
preprint, with A. Sommariva
Appl. Math. Comput. 183 (2006), 10981107
 Numerical cubature on scattered
data by radial basis
functions
preprint, with A. Sommariva
Computing 76 (2006), 295310
 Fast summation of power series with coefficients analytic
at infinity
with A. Sommariva and R. Zanovello
Numer. Algorithms 27 (2001), 7787
 A new summation method for power series with rational
coefficients
with S. Dassie`and R. Zanovello
Math. Comp. 69 (2000), 749756
 Asymptotic summation of power series
preprint, with S. Dassie`and R. Zanovello
Numer. Math. 80 (1998), 6173