5 citations · 18 across the 31 of their papers we have counts for
31 papers
A simple algorithm for the summation of alternating series
Eleonora Denich, Paolo Novati, Alvise Sommariva
This paper deals with the computation of the sum of alternating series, whose general terms can be expressed by means of analytic functions. After rewriting the series as a weighte…
Comparing algebraic cubature rules on spline curved elements
A. Sommariva, M. Vianello
We compare four methods for the construction of algebraic cubature rules on planar elements, whose boundary is tracked by splines. The methods, that we have developed over the last…
On modified anti-Gaussian rules for Jacobi weight functions
Eleonora Denich, Paolo Novati, Alvise Sommariva
Anti-Gaussian formulas represent an efficient tool for a dynamical estimation of the error of the underlying Gaussian rule. When applied to the Jacobi weight function it is known t…
On the role of weak Marcinkiewicz-Zygmund constants in polynomial approximation by orthogonal bases
Congpei An, Alvise Sommariva, Marco Vianello
We compute numerically the Marcinkiewicz-Zygmund constants of cubature rules, with a special attention to their role in polynomial approximation by orthogonal bases. We test…
ORTHOCUB: integral and differential cubature rules by orthogonal moments
Laura Rinaldi, Alvise Sommariva, Marco Vianello
We discuss a numerical package, named ORTHOCUB, for the computation of linear functionals of both integral and differential type on multivariate polynomial spaces. The weighted sum…
Effective numerical integration on complex shaped elements by discrete signed measures
Laura Rinaldi, Alvise Sommariva, Marco Vianello
We discuss a cheap and stable approach to polynomial moment-based compression of multivariate measures by discrete signed measures. The method is based on the availability of an or…
Unisolvence of randomized MultiQuadric Kansa collocation for convection-diffusion with mixed boundary conditions
Maryam Mohammadi, Alvise Sommariva, Marco Vianello
We make a further step in the open problem of unisolvence for unsymmetric Kansa collocation, proving that the MultiQuadric Kansa method with fixed collocation points and random fic…
Cheap and stable quadrature on polyhedral elements
Alvise Sommariva, Marco Vianello
We discuss a cheap tetrahedra-free approach to the numerical integration of polynomials on polyhedral elements, based on hyperinterpolation in a bounding box and Chebyshev moment c…
Polynomial meshes on algebraic sets
Leokadia Bialas-Ciez, Agnieszka Kowalska, Alvise Sommariva
Polynomial meshes (called sometimes "norming sets") allow us to estimate the supremum norm of polynomials on a fixed compact set by the norm on its discrete subset. We give a gener…
Unisolvence of Kansa collocation for elliptic equations by polyharmonic splines with random fictitious centers
Maryam Mohammadi, Alvise Sommariva, Marco Vianello
We make a further step in the unisolvence open problem for unsymmetric Kansa collocation, proving nonsingularity of Kansa matrices with polyharmonic splines and random fictitious c…
Unisolvence of unsymmetric random Kansa collocation by Gaussians and other analytic RBF vanishing at infinity
Alvise Sommariva, Marco Vianello
We give a short proof of almost sure invertibility of unsymmetric random Kansa collocation matrices by a class of analytic RBF vanishing at infinity, for the Poisson equation with…
Random sampling and polynomial-free interpolation by Generalized MultiQuadrics
A. Sommariva, M. Vianello
We prove that interpolation matrices for Generalized MultiQuadrics (GMQ) of order greater than one are almost surely nonsingular without polynomial addition, in any dimension and w…
Nonsingularity of unsymmetric Kansa matrices: random collocation by MultiQuadrics and Inverse MultiQuadrics
R. Cavoretto, F. Dell'Accio, A. De Rossi +2
Unisolvence of unsymmetric Kansa collocation is still a substantially open problem. We prove that Kansa matrices with MultiQuadrics and Inverse MultiQuadrics for the Dirichlet prob…
Unisolvence of random Kansa collocation by Thin-Plate Splines for the Poisson equation
Francesco Dell'Accio, Alvise Sommariva, Marco Vianello
Existence of sufficient conditions for unisolvence of Kansa unsymmetric collocation for PDEs is still an open problem. In this paper we make a first step in this direction, proving…
Numerical cubature and hyperinterpolation over Spherical Polygons
Alvise Sommariva
The purpose of this work is to introduce a strategy for determining the nodes and weights of a low-cardinality positive cubature formula nearly exact for polynomials of a given deg…
Polynomial-free unisolvence of polyharmonic splines with odd exponent by random sampling
Alvise Sommariva, Marco Vianello
In a recent paper almost sure unisolvence of RBF interpolation at random points with no polynomial addition was proved, for Thin-Plate Splines and Radial Powers with noninteger exp…
A note on polynomial-free unisolvence of polyharmonic splines at random points
Len Bos, Alvise Sommariva, Marco Vianello
In this note we prove almost sure unisolvence of RBF interpolation on randomly distributed sequences by a wide class of polyharmonic splines (including Thin-Plate Splines), without…
Evaluating Lebesgue constants by Chebyshev polynomial meshes on cube, simplex and ball
L. Bialas-Ciez, D. J. Kenne, A. Sommariva +1
We show that product Chebyshev polynomial meshes can be used, in a fully discrete way, to evaluate with rigorous error bounds the Lebesgue constant, i.e. the maximum of the Lebesgu…
Chebyshev admissible meshes and Lebesgue constants of complex polynomial projections
Leokadia Bialas-Ciez, Dimitri Jordan Kenne, Alvise Sommariva +1
We construct admissible polynomial meshes on piecewise polynomial or trigonometric curves of the complex plane, by mapping univariate Chebyshev points. Such meshes can be used for…
Numerical cubature on scattered data by adaptive interpolation
R. Cavoretto, F. Dell'Accio, A. De Rossi +4
We construct cubature methods on scattered data via resampling on the support of known algebraic cubature formulas, by different kinds of adaptive interpolation (polynomial, RBF, P…
Hybrid hyperinterpolation over general regions
Congpei An, Jiashu Ran, Alvise Sommariva
We present an -regularized discrete least squares approximation over general regions under assumptions of hyperinterpolation, named hybrid hyperinterpolation. Hybr…
Qsurf: compressed QMC integration on parametric surfaces
Giacomo Elefante, Alvise Sommariva, Marco Vianello
We discuss a bottom-up algorithm for Tchakaloff like compression of Quasi-MonteCarlo (QMC) integration on surfaces that admit an analytic parametrization.
Random sampling and unisolvent interpolation by almost everywhere analytic functions
Francesco Dell'Accio, Alvise Sommariva, Marco Vianello
We prove a.s. (almost sure) unisolvency of interpolation by continuous random sampling with respect to any given density, in spaces of multivariate a.e. (almost everywhere) analyti…
Compressed QMC volume and surface integration on union of balls
Giacomo Elefante, Alvise Sommariva, Marco Vianello
We discuss an algorithm for Tchakaloff-like compression of Quasi-MonteCarlo (QMC) volume/surface integration on union of balls (multibubbles). The key tools are Davis-Wilhelmsen th…