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Winter 1994 Homotopy Method for the Singular Symmetric Tridiagonal Eigenproblem
Kuiyuan Li, Tien-Yien Li
Missouri J. Math. Sci. 6(1): 34-46 (Winter 1994). DOI: 10.35834/1994/0601034


In this paper, a homotopy algorithm for finding some or all finite eigenvalues and corresponding eigenvectors of a real symmetric matrix pencil $(A,B)$ is presented, where $A$ is a symmetric tridiagonal matrix and $B$ is a diagonal matrix with $b_i \ge 0$, $i = 1, 2, \ldots , n$. It is shown that there are exactly $m$ ($m$ is the number of finite eigenvalues of $(A,B)$) disjoint, smooth homotopy paths connecting the trivial eigenpairs to the desired eigenpairs. And the eigenvalue curves are monotonic and easy to follow. The performance of the parallel version of our algorithm is presented.


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Kuiyuan Li. Tien-Yien Li. "Homotopy Method for the Singular Symmetric Tridiagonal Eigenproblem." Missouri J. Math. Sci. 6 (1) 34 - 46, Winter 1994.


Published: Winter 1994
First available in Project Euclid: 17 December 2019

zbMATH: 1097.65515
MathSciNet: MR1321973
Digital Object Identifier: 10.35834/1994/0601034

Rights: Copyright © 1994 Central Missouri State University, Department of Mathematics and Computer Science


Vol.6 • No. 1 • Winter 1994
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