Rectangular eigenvalue problems

2021/12/27 by Behnam Hashemi, Yuji Nakatsukasa, Hashemi, Behnam +3 · 2 citations
Computer Science · Mathematics · #47A75 #65F15 #65N35 #FOS: Mathematics #Mathematical functions and polynomials #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.2112.13698

openalex publication_date 2021/12/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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=infinity" of eigenvalue problems for quasimatrices. Numerical examples are presented as well as pointers to some related literature.

Cited by

• A Minimal Perturbation Approach For The Rectangular Multiparameter Eigenvalue Problem
• Quantum algorithm for solving generalized eigenvalue problems with application to the Schrödinger equation

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