caa a22 4500 605497133 CHVBK 20210128100539.0 cr unu---uuuuu 210128e20151201xx s 000 0 eng 10.1007/s10543-014-0537-6 doi (NATIONALLICENCE)springer-10.1007/s10543-014-0537-6 Fast computation of orthonormal basis for RBF spaces through Krylov space methods [Elektronische Daten] [Stefano De Marchi, Gabriele Santin] 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. Springer Science+Business Media Dordrecht, 2014 Interpolation nationallicence Positive definite functions nationallicence Matrix factorization nationallicence Fast computation nationallicence De Marchi Stefano Department of Mathematics, University of Padova, via Trieste 63, Padova, Italy aut Santin Gabriele Department of Mathematics, University of Padova, via Trieste 63, Padova, Italy aut BIT Numerical Mathematics Springer Netherlands 55/4(2015-12-01), 949-966 0006-3835 55:4<949 2015 55 10543 https://doi.org/10.1007/s10543-014-0537-6 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10543-014-0537-6 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- De Marchi Stefano Department of Mathematics, University of Padova, via Trieste 63, Padova, Italy aut NATIONALLICENCE 700 1- Santin Gabriele Department of Mathematics, University of Padova, via Trieste 63, Padova, Italy aut NATIONALLICENCE 773 0- BIT Numerical Mathematics Springer Netherlands 55/4(2015-12-01), 949-966 0006-3835 55:4<949 2015 55 10543