5 citations · 18 across the 31 of their papers we have counts for
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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…