Convergence of the Isometric Arnoldi Process

Authors:
S. Helsen;A. B. J. Kuijlaars;M. Van Barel
Affiliations:
-;-;-
Venue:
SIAM Journal on Matrix Analysis and Applications
Year:
2005

Citing 0
Cited 3

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On the Convergence of Rational Ritz Values

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Abstract

It is well known that the performance of eigenvalue algorithms such as the Lanczos and the Arnoldi methods depends on the distribution of eigenvalues. Under fairly general assumptions we characterize the region of good convergence for the isometric Arnoldi process. We also determine bounds for the rate of convergence and we prove sharpness of these bounds. The distribution of isometric Ritz values is obtained as the minimizer of an extremal problem. We use techniques from logarithmic potential theory in proving these results.