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Structured backward error and condition of generalized eigenvalue problems

Higham, D.J. and Higham, N.J. (1998) Structured backward error and condition of generalized eigenvalue problems. SIAM Journal on Matrix Analysis and Applications, 20 (2). pp. 493-512. ISSN 0895-4798

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Abstract

Backward errors and condition numbers are defined and evaluated for eigenvalues and eigenvectors of generalized eigenvalue problems. Both normwise and componentwise measures are used. Unstructured problems are considered first, and then the basic definitions are extended so that linear structure in the coefficient matrices (for example, Hermitian, Toeplitz, Hamiltonian, or band structure) is preserved by the perturbations.