Multiprocessor algorithm for the symmetric tridiagonal eigenvalue problem

Technical Report · Wed Jan 08 04:00:00 EST 1986

OSTI ID:7008081

Lo, S S; Philippe, B; Sameh, A

A multiprocessor algorithm for finding few or all eigenvalues and the corresponding eigenvectors of a symmetric tridiagonal matrix is presented. It is a pipelined variation of EISPACK routines - BISECT and TINVIT which consists of the three steps: isolation, extraction - inverse iteration, and partial orthogonalization. Multisections are performed for isolating the eigenvalues in a given interval, while bisection or the Zeroin method is used to extract these isolated eigenvalues. After the corresponding eigenvectors have been computed by inverse iteration, the modified Gram-Schmidt method is used to orthogonalize certain groups of these vectors. Experiments on the Alliant FX/8 and CRAY X-MP/48 multiprocessors show that this algorithm achieves high speedup over BISECT and TINVIT; in fact it is much faster than TQL2 when all the eigenvalues and eigenvectors are required.

• Research Organization: Illinois Univ., Urbana (USA). Center for Supercomputing Research and Development
• DOE Contract Number: FG02-85ER25001
• OSTI ID: 7008081
• Report Number(s): DOE/ER/25001-30; CSRD-568; ON: DE87002105
• Country of Publication: United States
• Language: English

Related Subjects

658000 -- Mathematical Physics-- (-1987)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
99 GENERAL AND MISCELLANEOUS
990200* -- Mathematics & Computers
COMPUTER CODES
COMPUTERS
CRAY COMPUTERS
DATA
EIGENVALUES
EXPERIMENTAL DATA
INFORMATION
ITERATIVE METHODS
MATRICES
NUMERICAL DATA
PARALLEL PROCESSING
PERFORMANCE TESTING
PROGRAMMING
T CODES
TESTING