On improving linear solver performance: a block variant of GMRES

Journal Article · Mon May 10 04:00:00 EDT 2004 · SIAM Journal on Scientific Computing

OSTI ID:881896

Baker, A H; Dennis, J M; Jessup, E R

The increasing gap between processor performance and memory access time warrants the re-examination of data movement in iterative linear solver algorithms. For this reason, we explore and establish the feasibility of modifying a standard iterative linear solver algorithm in a manner that reduces the movement of data through memory. In particular, we present an alternative to the restarted GMRES algorithm for solving a single right-hand side linear system Ax = b based on solving the block linear system AX = B. Algorithm performance, i.e. time to solution, is improved by using the matrix A in operations on groups of vectors. Experimental results demonstrate the importance of implementation choices on data movement as well as the effectiveness of the new method on a variety of problems from different application areas.

• Research Organization: Lawrence Livermore National Laboratory (LLNL), Livermore, CA
• Sponsoring Organization: USDOE
• DOE Contract Number: W-7405-ENG-48
• OSTI ID: 881896
• Report Number(s): UCRL-JRNL-204081
• Journal Information: SIAM Journal on Scientific Computing, Journal Name: SIAM Journal on Scientific Computing Journal Issue: 5 Vol. 27; ISSN 1064-8275; ISSN SJOCE3
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
ALGORITHMS
IMPLEMENTATION
PERFORMANCE
VECTORS