A multiprocessor algorithm for the symmetric tridiagonal Eigenvalue problem

Journal Article · Sun Mar 01 04:00:00 EST 1987 · SIAM J. Sci. Stat. Comput.; (United States)

DOI:https://doi.org/10.1137/0908019· OSTI ID:6574684

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 speed-up over BISECT and TINVIT; in fact it is much faster than TQL2 when all the eigenvalues and eigenvectors are required.

• Research Organization: Center for Supercomputing Research and Development, Univ. of Illinois, Urbana, IL
• OSTI ID: 6574684
• Journal Information: SIAM J. Sci. Stat. Comput.; (United States), Journal Name: SIAM J. Sci. Stat. Comput.; (United States) Vol. 8:2; ISSN SIJCD
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
990210* -- Supercomputers-- (1987-1989)
ALGORITHMS
ARRAY PROCESSORS
B CODES
COMPARATIVE EVALUATIONS
COMPUTER CODES
COMPUTERS
CRAY COMPUTERS
DATA-FLOW PROCESSING
DIGITAL COMPUTERS
E CODES
EIGENVALUES
EIGENVECTORS
ITERATIVE METHODS
MATHEMATICAL LOGIC
MATRICES
ORTHOGONAL TRANSFORMATIONS
PERFORMANCE
PROGRAMMING
SUPERCOMPUTERS
SYMMETRY
T CODES
TRANSFORMATIONS