5 citations · 24 across the 21 of their papers we have counts for
21 papers
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…
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…
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…
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…
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…
TetraFreeQ: tetrahedra-free quadrature on polyhedral elements
Alvise Sommariva, Marco Vianello
In this paper we provide a tetrahedra-free algorithm to compute low-cardinality quadrature rules with a given degree of polynomial exactness, positive weights and interior nodes on…
InRS: implementing the indicator function of NURBS-shaped planar domains
Alvise Sommarivaa, Marco Vianello
We provide an algorithm that implements the indicator function of NURBS-shaped planar domains, tailored to the fast computation on huge point clouds, together with the correspondin…
Numerical differentiation on scattered data through multivariate polynomial interpolation
Francesco Dell'Accio, F. Di Tommaso, N. Siar +1
We discuss a pointwise numerical differentiation formula on multivariate scattered data, based on the coefficients of local polynomial interpolation at Discrete Leja Points, writte…
Discrete norming inequalities on sections of sphere, ball and torus
Alvise Sommariva, Marco Vianello
By discrete trigonometric norming inequalities on subintervals of the period, we construct norming meshes with optimal cardinality growth for algebraic polynomials on sections of s…
Optimal polynomial meshes and Caratheodory-Tchakaloff submeshes on the sphere
Paul Leopardi, Alvise Sommariva, Marco Vianello
Using the notion of Dubiner distance, we give an elementary proof of the fact that good covering point configurations on the 2-sphere are optimal polynomial meshes. From these we e…
Caratheodory-Tchakaloff Subsampling
Federico Piazzon, Alvise Sommariva, Marco Vianello
We present a brief survey on the compression of discrete measures by Caratheodory-Tchakaloff Subsampling, its implementation by Linear or Quadratic Programming and the application…
Trivariate polynomial approximation on Lissajous curves
Len Bos, Stefano De Marchi, Marco Vianello
We study Lissajous curves in the 3-cube, that generate algebraic cubature formulas on a special family of rank-1 Chebyshev lattices. These formulas are used to construct trivariate…
Geometric Weakly Admissible Meshes, Discrete Least Squares Approximations and Approximate Fekete Points
Len Bos, Jean-Paul Calvi, Norm Levenberg +2
Using the concept of Geometric Weakly Admissible Meshes together with an algorithm based on the classical QR factorization of matrices, we compute efficient points for discrete mul…
New cubature formulae and hyperinterpolation in three variables
Stefano De Marchi, Marco Vianello, Yuan Xu
A new algebraic cubature formula of degree for the product Chebyshev measure in the -cube with nodes is established. The new formula is then applied…
Bivariate Lagrange interpolation at the Padua points: the ideal theory approach
Len Bos, Stefano De Marchi, Marco Vianello +1
Padua points is a family of points on the square given by explicit formulas that admits unique Lagrange interpolation by bivariate polynomials. The interpolation polynom…