Low-rank approximation of integral operators by using the Green formula and quadrature View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2013-11

AUTHORS

Steffen Börm, Jessica Gördes

ABSTRACT

Approximating integral operators by a standard Galerkin discretisation typically leads to dense matrices. To avoid the quadratic complexity it takes to compute and store a dense matrix, several approaches have been introduced including -matrices. The kernel function is approximated by a separable function, this leads to a low rank matrix. Interpolation is a robust and popular scheme, but requires us to interpolate in each spatial dimension, which leads to a complexity of for -th order. Instead of interpolation we propose using quadrature on the kernel function represented with Green’s formula. Due to the fact that we are integrating only over the boundary, we save one spatial dimension compared to the interpolation method and get a complexity of . More... »

PAGES

567-592

Journal

TITLE

Numerical Algorithms

ISSUE

3

VOLUME

64

Author Affiliations

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s11075-012-9679-2

DOI

http://dx.doi.org/10.1007/s11075-012-9679-2

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1024647692


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