A BLOCK VARIANT OF THE GMRES METHOD ON MASSIVELY-PARALLEL PROCESSORS

This paper presents a block variant of the GMRES method for solving ge neral unsymmetric linear systems. This algorithm generates a transform ed 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 demonstrate that this algorithm ca n be more efficient than the standard GMRES method on a cache based si ngle CPU computer with optimized BLAS kernels, Furthermore, the gain i n efficiency is more significant on MPPs due to both efficient block o perations and efficient block data communications. Preliminary numeric al results on some real-world problems also show that this algorithm m ay be stable up to some reasonable block size.