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math.NA2024
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…
math.NA2024★ 1 cited
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…
math.NA2024★ 3 cited
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…