Arnoldi versus nonsymmetric Lanczos algorithms for solving matrix eigenvalue problems
A comparison is made between the Arnoldi and the nonsymmetric Lanczos process for computing eigenvalues of nonsymmetric matrices. It is shown that the two processes are similar in the sense that any type of convergence behaviour obtained in exact arithmetic by the nonsymmetric Lanczos process may also be obtained by the Arnoldi procedure applied to another, but related, matrix and a different starting vector. Naturally, one is more interested in a comparison when both algorithms are applied to the same matrix and starting vector. From this, numerical experiments were designed and carried out. The results indicate that the nonsymmetric Lanczos procedure might be less sensitive to deviations from normality, but that the Arnoldi process might converge faster for nearly normal matrices.
scientific article; zbMATH DE number 934132
scientific article