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A matrix analysis of Arnoldi and Lanczos methods. (English) Zbl 0918.65024

The author presents a matrix analysis of the Arnoldi and Lanczos methods for approximating eigenpairs of a non-normal matrix. A new relation between the matrix representation of the two methods is defined to relate the corresponding eigenvalues and eigenvectors. Finally, backward error analysis is used to theoretically justify some unexpected experimental behaviour of non-normal matrices and in particular of banded Toeplitz matrices.
Reviewer: P.Narain (Bombay)

MSC:

65F15 Numerical computation of eigenvalues and eigenvectors of matrices

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