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Homotopy algorithm for symmetric eigenvalue problems. (English) Zbl 0653.65025

The homotopy method can be used to solve eigenvalue-eigenvector problems. The purpose of this paper is to report the numerical experience of the homotopy method of computing eigenpairs for real symmetric tridiagonal matrices together with a couple of new theoretical results. In practice, it is rarely of any interest to compute all the eigenvalues. The homotopy method, having the order preserving property, can provide any specific eigenvalue without calculating any other eigenvalues. Besides this advantage, we note that the homotopy algorithm is to a large degree a parallel algorithm. Numerical experimentation shows that the homotopy method can be very efficient especially for graded matrices.
Reviewer: T.Y.Li

MSC:

65F15 Numerical computation of eigenvalues and eigenvectors of matrices
65Y05 Parallel numerical computation

Software:

PITCON; EISPACK
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References:

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