Finding eigenvalues and eigenvectors of unsymmetric matrices using a hypercube multiprocessor

Conference · Thu Dec 31 23:00:00 EST 1987

OSTI ID:6983958

Geist, G A; Ward, R C; Davis, G J; Funderlic, R E

Distributed-memory algorithms for finding the eigenvalues and eigenvectors of a dense unsymmetric matrix are given. While several parallel algorithms have been developed for symmetric systems, little work has been done on the unsymmetric case. Our parallel implementation proceeds in three major steps: reduction of the original matrix to Hessenberg form, application of the implicit double-shift QR algorithm to compute the eigenvalues, and back transformations to compute the eigenvectors. Several modifications to our parallel QR algorithm, including ring communication and pipelining, are discussed and compared. Results and timings are given. 5 refs., 3 figs.

• Research Organization: Oak Ridge National Lab., TN (USA)
• DOE Contract Number: AC05-84OR21400
• OSTI ID: 6983958
• Report Number(s): CONF-880117-7; ON: DE89002311
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
990210 -- Supercomputers-- (1987-1989)
990230* -- Mathematics & Mathematical Models-- (1987-1989)
ALGORITHMS
CALCULATION METHODS
COMPUTERS
EFFICIENCY
EIGENVALUES
EIGENVECTORS
HYPERCUBE COMPUTERS
MATHEMATICAL LOGIC
MATRICES
NUMERICAL SOLUTION
PARALLEL PROCESSING
PROGRAMMING