Gaussian kernel quadrature at scaled Gauss–Hermite nodes
| Autor: | Simo Särkkä, Toni Karvonen |
|---|---|
| Přispěvatelé: | Sensor Informatics and Medical Technology, Department of Electrical Engineering and Automation, Aalto-yliopisto, Aalto University |
| Rok vydání: | 2019 |
| Předmět: |
Kernel quadrature
Hermite polynomials Computer Networks and Communications Applied Mathematics Gaussian Mercer eigendecomposition 010103 numerical & computational mathematics 01 natural sciences Quadrature (mathematics) 010101 applied mathematics Computational Mathematics symbols.namesake Tensor product Rate of convergence Gaussian quadrature Numerical integration Gaussian function symbols Applied mathematics 0101 mathematics Software Eigendecomposition of a matrix Mathematics Reproducing kernel Hilbert space |
| Zdroj: | BIT Numerical Mathematics. 59:877-902 |
| ISSN: | 1572-9125 0006-3835 |
| DOI: | 10.1007/s10543-019-00758-3 |
| Popis: | This article derives an accurate, explicit, and numerically stable approximation to the kernel quadrature weights in one dimension and on tensor product grids when the kernel and integration measure are Gaussian. The approximation is based on use of scaled Gauss–Hermite nodes and truncation of the Mercer eigendecomposition of the Gaussian kernel. Numerical evidence indicates that both the kernel quadrature and the approximate weights at these nodes are positive. An exponential rate of convergence for functions in the reproducing kernel Hilbert space induced by the Gaussian kernel is proved under an assumption on growth of the sum of absolute values of the approximate weights. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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