Performance and Accuracy of LAPACK's Symmetric TridiagonalEigensolvers

Journal Article · Thu Apr 19 04:00:00 EDT 2007 · SIAM Journal on Scientific Computing

OSTI ID:928868

Demmel, Jim W; Marques, Osni A; Parlett, Beresford N; Vomel, Christof

We compare four algorithms from the latest LAPACK 3.1 release for computing eigenpairs of a symmetric tridiagonal matrix. These include QR iteration, bisection and inverse iteration (BI), the Divide-and-Conquer method (DC), and the method of Multiple Relatively Robust Representations (MR). Our evaluation considers speed and accuracy when computing all eigenpairs, and additionally subset computations. Using a variety of carefully selected test problems, our study includes a variety of today's computer architectures. Our conclusions can be summarized as follows. (1) DC and MR are generally much faster than QR and BI on large matrices. (2) MR almost always does the fewest floating point operations, but at a lower MFlop rate than all the other algorithms. (3) The exact performance of MR and DC strongly depends on the matrix at hand. (4) DC and QR are the most accurate algorithms with observed accuracy O({radical}ne). The accuracy of BI and MR is generally O(ne). (5) MR is preferable to BI for subset computations.

• Research Organization: COLLABORATION - UCBerkeley
• DOE Contract Number: AC02-05CH11231
• OSTI ID: 928868
• Report Number(s): LBNL--62584; BnR: 830404000
• Journal Information: SIAM Journal on Scientific Computing, Journal Name: SIAM Journal on Scientific Computing Journal Issue: 3 Vol. 30; ISSN 1064-8275; ISSN SJOCE3
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
ACCURACY
ALGORITHMS
COMPUTER ARCHITECTURE
EVALUATION
MATRICES
PERFORMANCE
VELOCITY