A Multiprocessor Algorithm for the Symmetric Tridiagonal Eigenvalue Problem

• DOI: 10.1137/0908019
• Publication Date: 2005-03-01T03:33:28Z
• Authors: Sy-Shin Lo; Bernard Philippe; Ahmed Sameh
• Keywords: Bisection method; Matrix (chemical analysis); Orthogonalization

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