Zobrazeno 1 - 10
of 306
pro vyhledávání: '"Vianello, Marco"'
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 centers, for second-order elliptic equations with mixed boundary condit
Externí odkaz:
http://arxiv.org/abs/2410.03279
Autor:
Sommariva, Alvise, Vianello, Marco
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
Externí odkaz:
http://arxiv.org/abs/2405.18550
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 that unsymmetric collocation matrices with Thin-Plate Splines for the
Externí odkaz:
http://arxiv.org/abs/2403.06646
Autor:
Sommariva, Alvise, Vianello, Marco
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 exponent. The proving technique left unsolved the case of odd exponents.
Externí odkaz:
http://arxiv.org/abs/2401.13322
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 polynomial addition.
Externí odkaz:
http://arxiv.org/abs/2312.13710
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 polynomial least-squares, for the extraction of Fekete-like and Leja-l
Externí odkaz:
http://arxiv.org/abs/2311.06511
We discuss a bottom-up algorithm for Tchakaloff like compression of Quasi-MonteCarlo (QMC) integration on surfaces that admit an analytic parametrization.
Externí odkaz:
http://arxiv.org/abs/2304.08090
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) analytic functions. Examples are given concerning polynomial and RBF approxim
Externí odkaz:
http://arxiv.org/abs/2303.14074
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 theorem on the so-called Tchakaloff sets for positive linear functionals
Externí odkaz:
http://arxiv.org/abs/2303.01460
Autor:
Sommariva, Alvise, Vianello, Marco
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 a polyhedral element with arbitrary shape. The key tools are the noti
Externí odkaz:
http://arxiv.org/abs/2211.16620