A block Jacobi method on a mesh of processors

✍ Scribed by Giménez, D.; Hernández, V.; van de Geijn, R.; Vidal, A. M.

• Publisher: John Wiley and Sons
• Year: 1997
• Tongue: English
• Weight: 323 KB
• Volume: 9
• Category: Article
• ISSN: 1040-3108
• DOI: 10.1002/(sici)1096-9128(199705)9:5<391::aid-cpe259>3.0.co;2-b

✦ Synopsis

In this paper, we study the parallelization of the Jacobi method to solve the symmetric eigenvalue problem on a mesh of processors. To solve this problem obtaining a theoretical efficiency of 100% it is necessary to exploit the symmetry of the matrix. The only previous algorithm we know exploiting the symmetry on multicomputers is that of van de Geijn (1991), but that algorithm uses a storage scheme adequate for a logical ring of processors, so having a low scalability. In this paper we show how matrix symmetry can be exploited on a logical mesh of processors obtaining a higher scalability than that obtained with van de Geijn's algorithm. In addition, we show how the storage scheme exploiting the symmetry can be combined with a scheme by blocks to obtain a highly efficient and scalable Jacobi method for solving the symmetric eigenvalue problem for distributed memory parallel computers. We report performance results from the Intel Touchstone Delta, the iPSC/860, the Alliant FX/80 and the PARSYS SN-1040.