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A matrix analysis of Arnoldi and Lanczos methods
Authors:V Simoncini
Institution:(1) Istituto di Analisi Numerica, Consiglio Nazionale delle Ricerche, via Abbiategrasso, 209, I-27100 Pavia, Italy; e-mail: val@dragon.ian.pv.cnr.it , IT
Abstract:Summary. In this paper we propose a matrix analysis of the Arnoldi and Lanczos procedures when used for approximating the eigenpairs of a non-normal matrix. By means of a new relation between the respective representation matrices, we relate the corresponding eigenvalues and eigenvectors. Moreover, backward error analysis is used to theoretically justify some unexpected experimental behaviors of non-normal matrices and in particular of banded Toeplitz matrices. Received June 19, 1996 / Revised version received November 3, 1997
Keywords:Mathematics Subject Classification (1991):65F15
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