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## 2007.222: A Chart of Backward Errors for Singly and Doubly Structured Eigenvalue Problems

2007.222: Françoise Tisseur (2003) A Chart of Backward Errors for Singly and Doubly Structured Eigenvalue Problems. SIAM Journal on Matrix Analysis and Applications, 24 (3). pp. 877-897. ISSN 1095-7162

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## Abstract

We present a chart of structured backward errors for approximate eigenpairs of singly and doubly structured eigenvalue problems. We aim to give, wherever possible, formulae that are inexpensive to compute so that they can be used routinely in practice. We identify a number of problems for which the structured backward error is within a factor $\sqrt{2}$ of the unstructured backward error. This paper collects, unifies, and extends existing work on this subject.

Item Type: Article eigenvalue; backward error; condition number; eigenvector; symmetric matrix; Hermitian matrix; skew-symmetric matrix; skew-Hermitian matrix; symplectic matrix; conjugate symplectic matrix; Hamiltonian matrix MSC 2000 > 15 Linear and multilinear algebra; matrix theoryMSC 2000 > 65 Numerical analysis 2007.222 Ms Helen Kirkbright 04 December 2007