A Parallel Divide and Conquer Algorithm for the Generalized Real Symmetric Definite Tridiagonal Eigenproblem
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Authors
Borges, Carlos F.
Gragg, William B.
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Date of Issue
1993
Date
1993
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en_US
Abstract
We develop a parallel divide and conquer algorithm, by extention, for the generalized real symmetric definite tridiagonal eigenproblem. The algorithm employs techniques first proposed by Gu and Eisenstat to prevent loss of orthogonality in the computed eigenvectors for the modification algorithm. We examine numerical stability and adapt the insightful error analysis of Gu and Eisenstat to the arrow case. The algorithm incorporates an elegant zero funder with global monotone cubic convergence that has performed well in numerical experiments. A complete set of tested matlab routines implementing the algorithm is available on request from the authors.
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Article
Description
Both authors were supported by direct grant from the Naval Postgraduate School. The second author also acknowledges support from the Interdisciplinary Project Center for Supercomputing at the ETH, Zurich.
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Applied Mathematics
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Citation
Numerical Linear Algebra and Scientific Computing, (L. Reichel, A. Ruttan, and R.S. Varga, eds.), de Gruyter, Berlin, 1993, pp. 11-29.
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This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.