The Parallel Solution of Triangular Systems of Linear Equations

We present a parallel algorithm for solving triangular syst ems of linear equations on distributed-memory multiprocessor ma chines. The parallelism is achieved by partitioning the rows of the c o fficient matrix in segments of a fixed size and distributing these sets in a wrap-around fashion among the processors, connected in a ring. The granu la ity of the algorithm is controlled by varying the segment size. The algorithm is compared to other previously published alg orithms and is shown to provide a better performance. To be presented at the 2nd Symposium in High Performance Comp uting, 7-9 October 1991, Montpellier, France.