Structured backward error and condition of generalized eigenvalue problems

Backward errors and condition numbers are defined and evaluated for eigenva lues and eigenvectors of generalized eigenvalue problems. Both normwise and componentwise measures are used. Unstructured problems are considered firs t, 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.