ERROR ANALYSIS OF THE LANCZOS-ALGORITHM FOR THE NONSYMMETRIC EIGENVALUE PROBLEM

This paper presents an error analysis of the Lanczos algorithm in fini te-precision arithmetic for solving the standard nonsymmetric eigenval ue problem, if no breakdown occurs. An analog of Paige's theory on the relationship between the loss of orthogonality among the Lanczos vect ors and the convergence of Ritz values in the symmetric Lanczos algori thm is discussed. The theory developed illustrates that in the nonsymm etric Lanczos scheme, if Ritz values are well conditioned, then the lo ss of biorthogonality among the computed Lanczos vectors implies the c onvergence of a group of Ritz triplets in terms of small residuals. Nu merical experimental results confirm this observation.