An Implementation of the Look-Ahead Lanczos Algorithm for Non-Hermitian Matrices

Citations Over TimeTop 1% of 1993 papers

Abstract

The nonsymmetric Lanczos method can be used to compute eigenvalues of large sparse non-Hermitian matrices or to solve large sparse non-Hermitian linear systems. However, the original Lanczos algorithm is susceptible to possible breakdowns and potential instabilities. An implementation is presented of a look-ahead version of the Lanczos algorithm that, except for the very special situation of an incurable breakdown, overcomes these problems by skipping over those steps in which a breakdown or near-breakdown would occur in the standard process. The proposed algorithm can handle look-ahead steps of any length and requires the same number of matrix-vector products and inner products as the standard Lanczos process without look-ahead.

Related Papers

• → The Convergence of Generalized Lanczos Methods for Large Unsymmetric Eigenproblems(1995)63 cited
• → Computing resonance energies, widths, and wave functions using a Lanczos method in real arithmetic(2005)16 cited
• → Changing poles in the rational Lanczos method for the Hermitian eigenvalue problem(2000)13 cited
• An Implementation of the Look-Ahead Lanczos Algorithm for Non-Hermitian Matrices(1991)