Inclusion of eigenvalues of general eigenvalue problems for matrices

Inclusion of Eigenvalues of General Eigenvalue Problems for Matrices. In this paper, a procedure for calculating bounds to eigenvalues of general matrix eigenvalue problems is proposed. The procedure is based on Temple quotients and their generalization by Lehmann, in connection with interval arithmetic. Numerical examples illustrate the fact that bounds for multiple or clustered eigenvalues can be calculated as well.