Rectangular eigenvalue problems

Journal article

Abstract:: Often the easiest way to discretize an ordinary or partial differential equation is by a rectangular numerical method, in which n basis functions are sampled at m ≫ n collocation points. We show how eigenvalue problems can be solved in this setting by QR reduction to square matrix generalized eigenvalue problems. The method applies equally in the limit “m = ∞” of eigenvalue problems for quasimatrices. Numerical examples are presented as well as pointers to related literature.

Files:: Hashemi_et_al_2022_Rectangular_eigenvalue_problems.pdf

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Language:: English
Keywords:: Helmholtz equation

Fourier extension

eigenvalue problems

FFR

method of fundamental solutions

Vandermonde with Arnoldi

quasimatrix

spectral methods

lightning solver
Pubs id:: 1230997
Local pid:: pubs:1230997
Deposit date:: 2022-10-21

Copyright holder:: Hashemi et al.
Rights statement:: © The Author(s) 2022. Open Access. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

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