AN OPTIMAL ALGORITHM FOR GAUSSIAN-ELIMINATION OF BAND MATRICES ON AN MIMD COMPUTER

This paper describes a parallel algorithm for the LU decomposition of band matrices using Gaussian elimination. The matrix dimension is n × n with 2r-1 diagonals. In the case when 1 {slanted equal to or less-than} r ≤ 2 p an optimal number of the processors, p, is determined according to the equation p = [(r +1)/2]. When 2 p ≤ r ≤ n a number of processors, p, statged by Veldhorst is adopted (see [7]). For band matrix with 2r-1 diagonals (1 ≤ r ≤ 2p) the task scheduling procedure with the aim to obtain maximal parallelism in system operation, i.e. good load balancing, is defined. The architecture of the system is of MIMD type. The connection between the processors is realised via a common bus. Communication and synchronization is performed by message passing technique. © 1990.