A block variant of the GMRES method on massively parallel processors

✍ Scribed by Guangye Li

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 956 KB
• Volume: 23
• Category: Article
• ISSN: 0167-8191
• DOI: 10.1016/s0167-8191(97)00004-5

✦ Synopsis

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 demonstrate 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. Preliminary numerical results on some real-world problems also show that this algorithm may be stable up to some reasonable block size.