A block variant of the GMRES method on massively parallel processors

Conference · Tue Dec 31 04:00:00 EST 1996

DOI:https://doi.org/10.1016/S0167-8191(97)00004-5· OSTI ID:433335

Li, Guangye ^[1]

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1. Cray Research, Inc., Eagan, MN (United States)

This paper presents a block variant of the GMRES method for solving general unsymmetric linear systems. This algorithm generates a transformed Hessenberg matrix by solely using block matrix operations and block data communications. It is shown that this algorithm with block size s, denoted by BVGMRES(s,m), is theoretically equivalent to the GMRES(s*m) method. The numerical results show that this algorithm can be more efficient than the standard GMRES method on a cache based single CPU computer with optimized BLAS kernels. Furthermore, the gain in efficiency is more significant on MPPs due to both efficient block operations and efficient block data communications. Our numerical results also show that in comparison to the standard GMRES method, the more PEs that are used on an MPP, the more efficient the BVGMRES(s,m) algorithm is.

• Research Organization: Front Range Scientific Computations, Inc., Lakewood, CO (United States)
• OSTI ID: 433335
• Report Number(s): CONF-9604167--Vol.1; ON: DE96015306
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
ALGORITHMS
EFFICIENCY
ITERATIVE METHODS
PARALLEL PROCESSING