Arnoldi versus Nonsymmetric Lanczos Algorithms
for Solving Nonsymmetric Matrix Eigenvalue Problems
Arnoldi versus Nonsymmetric Lanczos Algorithms
for Solving Nonsymmetric Matrix Eigenvalue Problems
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Date
1998-10-15
Authors
Cullum, Jane K.
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Abstract
We obtain several results which may be useful in determining the
convergence behavior of eigenvalue algorithms based upo n Arnoldi and
nonsymmetric Lanczos recursions. We derive a relationship between
nonsymmetric Lanczos eigenvalue procedures and Arnoldi eigenvalue
procedures. We demonstrate that the Arnoldi recursions preserve a
property which characterizes normal matrices, and that if we could
determine the appropriate starting vectors, we could mimic the
nonsymmetric Lanczos eigenvalue convergence on a general diagonalizable
matrix by its convergence on related normal matrices. Using a unitary
equivalence for each of these Krylov subspace methods, we define sets of
test problems where we can easily vary certain spectral properties of the
matrices. We use these and other test problems to examine the behavior of
an Arnoldi and of a nonsymmetric Lanczos procedure.
(Also cross-referenced as UMIACS-TR-95-123)