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

Tisseur, Françoise (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

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.