Gaussian kernel quadrature at scaled Gauss–Hermite nodes

Tutkimustuotos: Lehtiartikkeli

Standard

Gaussian kernel quadrature at scaled Gauss–Hermite nodes. / Karvonen, Toni; Särkkä, Simo.

julkaisussa: BIT - Numerical Mathematics, 2019, s. 877–902.

Tutkimustuotos: Lehtiartikkeli

Harvard

APA

Vancouver

Author

Bibtex - Lataa

@article{d2d9537b2baa4ef3aca6ad49810c9c12,
title = "Gaussian kernel quadrature at scaled Gauss–Hermite nodes",
abstract = "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.",
keywords = "Numerical integration, Kernel quadrature, Gaussian quadrature, Mercer eigendecomposition",
author = "Toni Karvonen and Simo S{\"a}rkk{\"a}",
year = "2019",
doi = "10.1007/s10543-019-00758-3",
language = "English",
pages = "877–902",
journal = "BIT - Numerical Mathematics",
issn = "0006-3835",
publisher = "Springer Netherlands",

}

RIS - Lataa

TY - JOUR

T1 - Gaussian kernel quadrature at scaled Gauss–Hermite nodes

AU - Karvonen, Toni

AU - Särkkä, Simo

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

KW - Numerical integration

KW - Kernel quadrature

KW - Gaussian quadrature

KW - Mercer eigendecomposition

U2 - 10.1007/s10543-019-00758-3

DO - 10.1007/s10543-019-00758-3

M3 - Article

SP - 877

EP - 902

JO - BIT - Numerical Mathematics

JF - BIT - Numerical Mathematics

SN - 0006-3835

ER -

ID: 33799135