caa a22 4500 477074952 CHVBK 20180405111437.0 cr unu---uuuuu 170330e19961201xx s 000 0 eng 10.1007/BF02900879 doi (NATIONALLICENCE)springer-10.1007/BF02900879 Li Guanye Cray Research, Inc, 655F Lone Oak Drive, 55121, Eagan, MN, USA aut A block varaint of the GMRES method for unsymmetric linear systems [Elektronische Daten] [Guanye Li] Iterative methods that take advantage of efficient block operations and block communications are popular research topics in parallel computation. These methods are especially important on Massively Parallel Processors (MPP). This paper presents a block variant of the GMRES method for solving general unsymmetric linear systems. It is shown that the new algorithm with block sizes, 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 besed 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. Springer, 1996 iterative method nationallicence unsymmetric linear system nationallicence block algorithm nationallicence parallel computation nationallicence 65F10 nationallicence Wuhan University Journal of Natural Sciences Wuhan University 1/3-4(1996-12-01), 508-514 1007-1202 1:3-4<508 1996 1 11859 https://doi.org/10.1007/BF02900879 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02900879 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Li Guanye Cray Research, Inc, 655F Lone Oak Drive, 55121, Eagan, MN, USA aut NATIONALLICENCE 773 0- Wuhan University Journal of Natural Sciences Wuhan University 1/3-4(1996-12-01), 508-514 1007-1202 1:3-4<508 1996 1 11859 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer