Abstract

The Behaviour of the Finite Precision Lanczos Algorithm J.M. Zemke The symmetric Lanczos algorithm is one of the basic tools for the computation of parts of the spectrum of linear and nonlinear selfadjoint operators. The convergence properties of the Lanczos process in exact aritmetic are well known, but the properties of the finite precision algorithm are despite the results of Paige [1] less well known. It is shown that the convergence in symmetric finite precision Lanczos algorithms can be described in a more global framework including the exact case. Error analysis and numerical experiments suggest that three phases of convergence to an eigenpair should be distinguished. From the error analysis it is obvious that the observed behaviour only weekly depends on the used recurrence. The obtained results are used to enlighten the behaviour of the symmetric finite precision Lanczos algorithm with various reorthogonalization techniques. References [1] Paige, C.C. The Computation of Eigenvalues and Eigenvectors of Very Large Sparse Matrices. PhD thesis, University of London, 1971.

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