Unisolvence of unsymmetric random Kansa collocation by Gaussians and other analytic RBF vanishing at infinity

Fuente: arXiv
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Main Authors: Sommariva, Alvise, Vianello, Marco
Format: Preprint
Published: 2024
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author Sommariva, Alvise
Vianello, Marco
author_facet Sommariva, Alvise
Vianello, Marco
contents 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 Dirichlet boundary conditions. Such a class includes popular Positive Definite instances such as Gaussians, Generalized Inverse MultiQuadrics and Matern RBF. The proof works on general domains in any dimension, with any distribution of boundary collocation points and any continuous random distribution of internal collocation points.
format Preprint
id arxiv_https___arxiv_org_abs_2405_18550
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Unisolvence of unsymmetric random Kansa collocation by Gaussians and other analytic RBF vanishing at infinity
Sommariva, Alvise
Vianello, Marco
Numerical Analysis
Probability
65D12, 65N35
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 Dirichlet boundary conditions. Such a class includes popular Positive Definite instances such as Gaussians, Generalized Inverse MultiQuadrics and Matern RBF. The proof works on general domains in any dimension, with any distribution of boundary collocation points and any continuous random distribution of internal collocation points.
title Unisolvence of unsymmetric random Kansa collocation by Gaussians and other analytic RBF vanishing at infinity
topic Numerical Analysis
Probability
65D12, 65N35
url https://arxiv.org/abs/2405.18550