Precedence relationship minimization in numerically asymmetric matrix inverse factor calculations

A parallel algorithm for obtaining the inverse of the U triangular force of a non-numerically symmetric matrix A of dimension n × n is presented in this paper. The method proposed eliminates the precedence relationships involved with the backward substitution process, which is conventionally used to obtain the U^-1 factors. The inverse factors are obtained by performing the factorization on an extended matrix A_E, which is of dimension 2n × 2n. The method exploits the inherent parallelism in calculating the inverse factors during the forward sweep of the factorization process. Thus, a parallel factorization routine can be easily modified to calculate U^-1 in parallel. Unlike traditional methods involving precedence relations, which require 2p sequential steps (where p is the length of the longest factor path), the proposed method involves only p + 1 precedence relationships.