Eigenvalue Problems for Exponential-Type Kernels

Authors

Difeng Cai, Purdue University
Panayot S. Vassilevski, Portland State UniversityFollow

Sponsor

This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. LLNL-JRNL-755085. The second author was partially supported by NSF under grant DMS-1619640.

Published In

Computational Methods in Applied Mathematics

Document Type

Citation

Publication Date

1-1-2020

Abstract

We study approximations of eigenvalue problems for integral operators associated with kernel functions of exponential type. We show convergence rate |λ_k − λ_k,h| ≤ C_kh ² in the case of lowest order approximation for both Galerkin and Nyström methods, where h is the mesh size, λ_k and λ_k,h are the exact and approximate kth largest eigenvalues, respectively. We prove that the two methods are numerically equivalent in the sense that |λ_k,h^(G)-λ_k,h^(N)| ≤ Ch², where λ_k,h^(G) and λ_k,h^(N) denote the kth largest eigenvalues computed by Galerkin and Nyström methods, respectively, and C is a eigenvalue independent constant. The theoretical results are accompanied by a series of numerical experiments

Description

Copyright © 2011–2020 by Walter de Gruyter GmbH

Locate the Document

https://doi.org/10.1515/cmam-2018-0186

DOI

10.1515/cmam-2018-0186

Persistent Identifier

https://archives.pdx.edu/ds/psu/32519

Citation Details

Cai, D., & Vassilevski, P. S. (2020). Eigenvalue Problems for Exponential-Type Kernels. Computational Methods in Applied Mathematics, 20(1), 61-78.