A parallel scheme for the forward/backward substitutions in solving sparse linear equations

A parallel processing scheme for the solution of sparse linear network equations is presented. The scheme assumes an already factorized coefficient matrix and decomposes the forward/backward substitution operation into independent sequences. In doing this, sparse vector methods are used and the full right-hand side vector is considered as a sum of several sparse vectors. The developed scheme is simulated for various test systems, and the calculated gains in computation times are given. The results obtained are pertinent to the analysis of power-system problems