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Rectangular eigenvalue problems

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posted on 2023-08-02, 08:24 authored by B Hashemi, Y Nakatsukasa, LN Trefethen
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.

History

Author affiliation

School of Mathematical Sciences, University of Leicester

Version

  • VoR (Version of Record)

Published in

Advances in Computational Mathematics

Volume

48

Issue

6

Pagination

80

Publisher

Springer

issn

1019-7168

eissn

1572-9044

Copyright date

2022

Available date

2023-08-02

Language

en

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