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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…