Title

Rayleigh-Ritz Majorization Error Bounds of Mixed Type

Abstract

The absolute change in the Rayleigh quotient (RQ) for a Hermitian matrix with respect to vectors is bounded in terms of the norms of the residual vectors and the angle between vectors in [P. Zhu, M. E. Argentati, and A. V. Knyazev, SIAM J. Matrix Anal. Appl., 34 (2013), pp. 244-256]. We substitute multidimensional subspaces for the vectors and derive new bounds of absolute changes of eigenvalues of the matrix RQ in terms of singular values of residual matrices and principal angles between subspaces, using majorization. We show how our results relate to bounds for eigenvalues after discarding off-diagonal blocks or additive perturbations.

Department(s)

Computer Science

Comments

The work of the first author was supported by the National Science Foundation through grant DMS-1115734.

Keywords and Phrases

Eigenvalues and eigenfunctions; Error analysis; Matrix algebra; Angles; Eigen-value; Hermitians; Majorization; Rayleigh; Ritz; Subspaces; Vectors; Matrix

International Standard Serial Number (ISSN)

0895-4798; 1095-7162

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2017 Society for Industrial and Applied Mathematics, All rights reserved.

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