Publisher DOI: | 10.1016/j.laa.2005.06.009 | Title: | Eigenvalues, pseudospectrum and structured perturbations | Language: | English | Authors: | Rump, Siegfried M. ![]() |
Keywords: | Componentwise; Condition number; Eigenvalues; Normwise; Pseudospectrum; Structured perturbations | Issue Date: | 2006 | Publisher: | American Elsevier Publ. | Source: | Linear Algebra and Its Applications 413 (2-3 SPEC. ISS.): 567-593 (2006) | Abstract (english): | We investigate the behavior of eigenvalues under structured perturbations. We show that for many common structures such as (complex) symmetric, Toeplitz, symmetric Toeplitz, circulant and others the structured condition number is equal to the unstructured condition number for normwise perturbations, and prove similar results for real perturbations. An exception are complex skewsymmetric matrices. We also investigate componentwise complex and real perturbations. Here Hermitian and skew-Hermitian matrices are exceptional for real perturbations. Furthermore we characterize the structured (complex and real) pseudospectrum for a number of structures and show that often there is little or no significant difference to the usual, unstructured pseudospectrum. |
URI: | http://hdl.handle.net/11420/8878 | ISSN: | 0024-3795 | Journal: | Institute: | Zuverlässiges Rechnen E-19 | Document Type: | Article |
Appears in Collections: | Publications without fulltext |
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