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An Algorithm for Symmetric Tridiagonal Eigenproblems: Divide and Conquer with Homotopy Continuation
Journal article   Peer reviewed

An Algorithm for Symmetric Tridiagonal Eigenproblems: Divide and Conquer with Homotopy Continuation

Kuiyuan Li and Tien-Yien Li
SIAM journal on scientific computing, Vol.14(3), pp.735-751
05/1993
DOI: https://doi.org/10.1137/0914046
Web of Science ID: WOS:A1993KZ29800015

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15 Times Cited - Web of Science

Abstract

This paper presents a new algorithm for finding all the eigenvalues and corresponding eigenvectors of a symmetric tridiagonal matrix. The algorithm is based on the homotopy continuation approach coupled with the strategy of "divide and conquer." Evidenced by the numerical results, the algorithm given here provides a considerable advance over previous attempts to use the homotopy method for eigenvalue problems. Numerical comparisons of this algorithm with the methods in the widely used EISPACK library, as well as Cuppen's divide and conquer method, are presented. It appears that the algorithm is strongly competitive in terms of speed, accuracy, and orthogonality. The performance of the parallel version of this algorithm is also presented. The natural parallelism of the algorithm makes it an excellent candidate for a variety of advanced architectures.

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