Fast computation of orthonormal basis for RBF spaces through Krylov space methods
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| 024 | 7 | 0 | |a 10.1007/s10543-014-0537-6 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s10543-014-0537-6 | ||
| 245 | 0 | 0 | |a Fast computation of orthonormal basis for RBF spaces through Krylov space methods |h [Elektronische Daten] |c [Stefano De Marchi, Gabriele Santin] |
| 520 | 3 | |a 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. | |
| 540 | |a Springer Science+Business Media Dordrecht, 2014 | ||
| 690 | 7 | |a Interpolation |2 nationallicence | |
| 690 | 7 | |a Positive definite functions |2 nationallicence | |
| 690 | 7 | |a Matrix factorization |2 nationallicence | |
| 690 | 7 | |a Fast computation |2 nationallicence | |
| 700 | 1 | |a De Marchi |D Stefano |u Department of Mathematics, University of Padova, via Trieste 63, Padova, Italy |4 aut | |
| 700 | 1 | |a Santin |D Gabriele |u Department of Mathematics, University of Padova, via Trieste 63, Padova, Italy |4 aut | |
| 773 | 0 | |t BIT Numerical Mathematics |d Springer Netherlands |g 55/4(2015-12-01), 949-966 |x 0006-3835 |q 55:4<949 |1 2015 |2 55 |o 10543 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10543-014-0537-6 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s10543-014-0537-6 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a De Marchi |D Stefano |u Department of Mathematics, University of Padova, via Trieste 63, Padova, Italy |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Santin |D Gabriele |u Department of Mathematics, University of Padova, via Trieste 63, Padova, Italy |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t BIT Numerical Mathematics |d Springer Netherlands |g 55/4(2015-12-01), 949-966 |x 0006-3835 |q 55:4<949 |1 2015 |2 55 |o 10543 | ||