PUMA publications for /tag/fast%20Interpolation;%2042a82;Fri Jul 20 10:54:15 CEST 2018BIT Numerical Mathematics4949--966Fast computation of orthonormal basis for RBF spaces through Krylov
space methods55201515A23; 41A05; 42A82; 65Y20 Fast Interpolation; Matrix Positive computation; definite factorization; functions; vorlaeufig In recent years, in the setting of radial basis function, the study
of approximation algorithms has particularly focused on the construction
of (stable) bases for the associated Hilbert spaces. One of the ways
of describing such spaces and their properties is the study of a
particular integral operator and its spectrum. We proposed in a recent
work the so-called WSVD basis, which is strictly connected to the
eigen-decomposition of this operator and allows to overcome some
problems related to the stability of the computation of the approximant
for a wide class of radial kernels. Although effective, this basis
is computationally expensive to compute. In this paper we discuss
a method to improve and compute in a fast way the basis using methods
related to Krylov subspaces. After reviewing the connections between
the two bases, we concentrate on the properties of the new one, describing
its behavior by numerical tests.Fri Jul 20 10:54:28 CEST 2018BIT Numerical Mathematics4949--966Fast computation of orthonormal basis for RBF spaces through Krylov
space methods55201565Y20 vorlaeufig factorization; from:mhartmann definite 42A82; computation; Interpolation; 15A23; functions; 41A05; Fast Positive Matrix In recent years, in the setting of radial basis function, the study
of approximation algorithms has particularly focused on the construction
of (stable) bases for the associated Hilbert spaces. One of the ways
of describing such spaces and their properties is the study of a
particular integral operator and its spectrum. We proposed in a recent
work the so-called WSVD basis, which is strictly connected to the
eigen-decomposition of this operator and allows to overcome some
problems related to the stability of the computation of the approximant
for a wide class of radial kernels. Although effective, this basis
is computationally expensive to compute. In this paper we discuss
a method to improve and compute in a fast way the basis using methods
related to Krylov subspaces. After reviewing the connections between
the two bases, we concentrate on the properties of the new one, describing
its behavior by numerical tests.fast Interpolation; 42a82;Community for tag(s) fast Interpolation; 42a82;