A Block Arnoldi Method for Large Nonsymmetric Eigenvalue Problems

Research Report MRR98-062

A Block Arnoldi Method for Large Nonsymmetric Eigenvalue Problems

David L. Harrar II

Abstract: Arnoldi's method has proven to be a useful technique for locating a few of the dominant eigenvalues of a given nonsymmetric matrix. If the desired eigenvalues are multiple or clustered a block version of the method is often preferable; an additional advantage of block methods is that they enable the use of level-3 BLAS and hence may result in increased performance on high performance computer architectures due to increased computational density.

In this report we discuss a block Arnoldi method incorporating (1) shift-invert transformation for the location of non-extremal eigenvalues, (2) restarting so as to limit the size of Krylov subspaces, and (3) an implicit deflation scheme to inhibit reconvergence to already-converged eigenvalues.

The resulting algorithm has been implemented on the Fujitsu VPP300, and results are given for an application arising in the study of chemical reactions and one arising in the design of dielectric waveguides.

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Download paper:	PDF file (194K)
	gzipped DVI file (19K)

Download cover sheet:	PDF file (51K)
	DVI file (2K)