Parallel solution of the symmetric tridiagonal eigenproblem

Thesis/Dissertation · Sun Jan 01 04:00:00 EST 1989

OSTI ID:6155839

Jessup, E R

This thesis discusses methods for computing all eigenvalues and eigenvectors of a symmetric tridiagonal matrix on a distributed memory MIMD 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 speedup, and accuracy. Experiments on an iPSC hyper-cube 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 effects 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 adaptations 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)
• OSTI ID: 6155839
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
990200* -- Mathematics & Computers
ALGORITHMS
ARRAY PROCESSORS
COMPUTERS
DATA PROCESSING
DISTRIBUTED DATA PROCESSING
EIGENVALUES
EIGENVECTORS
HYPERCUBE COMPUTERS
MATHEMATICAL LOGIC
PARALLEL PROCESSING
PROCESSING
PROGRAMMING