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A look-ahead Lanczos algorithm for unsymmetric matrices. (English) Zbl 0564.65022
The Lanczos algorithm for nonsymmetric matrices is studied. It is shown how breakdown caused by a pair of corresponding basis vectors being orthogonal can be remedied by computing further vectors in the Krylov sequences. This corresponds to performing 2×2 pivots when factorizing the moment matrix, which may be indefinite for nonsymmetric eigenproblems. It is stated that when 2×2 pivots are insufficient to continue the process, all eigenvalues have converged. Results of a few numerical tests are reported.
Reviewer: A.Ruhe

MSC:
65F15Eigenvalues, eigenvectors (numerical linear algebra)