Parallel solution of the symmetric tridiagonal eigenproblem. Research report
This thesis discusses methods for computing all eigenvalues and eigenvectors of a symmetric tridiagonal matrix on a distributed-memory Multiple Instruction, Multiple Data multiprocessor. Only those techniques having the potential for both high numerical accuracy and significant large-grained parallelism are investigated. These include the QL method or Cuppen's divide and conquer method based on rank-one updating to compute both eigenvalues and eigenvectors, bisection to determine eigenvalues and inverse iteration to compute eigenvectors. To begin, the methods are compared with respect to computation time, communication time, parallel speed up, and accuracy. Experiments on an IPSC hypercube multiprocessor reveal that Cuppen's method is the most accurate approach, but bisection with inverse iteration is the fastest and most parallel. Because the accuracy of the latter combination is determined by the quality of the computed eigenvectors, the factors influencing the accuracy of inverse iteration are examined. This includes, in part, statistical analysis of the effect of a starting vector with random components. These results are used to develop an implementation of inverse iteration producing eigenvectors with lower residual error and better orthogonality than those generated by the EISPACK routine TINVIT. This thesis concludes with adaptions of methods for the symmetric tridiagonal eigenproblem to the related problem of computing the singular value decomposition (SVD) of a bidiagonal matrix.
- Research Organization:
- Yale Univ., New Haven, CT (USA). Dept. of Computer Science
- OSTI ID:
- 7230838
- Report Number(s):
- AD-A-215805/3/XAB; YALEU/DCS/RR-728
- Country of Publication:
- United States
- Language:
- English
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Multiprocessor algorithm for the symmetric tridiagonal eigenvalue problem
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Related Subjects
EIGENVALUES
COMPUTER CALCULATIONS
EIGENVECTORS
MATRICES
ACCURACY
ARRAY PROCESSORS
COMPUTER CODES
ERRORS
NUMERICAL ANALYSIS
NUMERICAL SOLUTION
PARALLEL PROCESSING
STATISTICS
VELOCITY
MATHEMATICS
PROGRAMMING
990200* - Mathematics & Computers