Variations on Arnoldi's method for computing eigenelements of large unsymmetric matrices

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Abstract

It is shown that the method of Arnoldi can be successfully used for solvinglarge unsymmetric eigenproblems. Like the symmetric Lanczos method, Arnoldi's algorithm realizes a projection process onto the Krylov subspace Km spanned by v1,Av1,...,Am-1v1, where v1 is the initial vector. We therefore study the convergence of the approximate eigenelements obtained by such a process. In particular, when the eigenvalues of A are real, we obtain bounds for the rates of convergence similar to those for the symmetric Lanczos algorithm. Some practical methods are presented in addition to that of Arnoldi, and several numerical experiments are described.

Original languageEnglish (US)
Pages (from-to)269-295
Number of pages27
JournalLinear Algebra and Its Applications
Volume34
Issue numberC
DOIs
StatePublished - Dec 1980

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