NEW PARALLEL ALGORITHMS FOR DIRECT SOLUTION OF SPARSE LINEAR-SYSTEMS - PART I - SYMMETRICAL COEFFICIENT MATRIX

In this paper, we propose a new parallel bidirectional algorithm, base d on Cholesky factorization, for the solution of sparse symmetric syst em of linear equations. Unlike the existing algorithms, the numerical factorization phase of our algorithm is carried out in such a manner t hat the entire back substitution component of the substitution phase i s replaced by a single step division. Since there is a substantial red uction in the time taken by the repeated execution of the substitution phase, our algorithm is particularly suited for the solution of syste ms with multiple b-vectors. The effectiveness of our algorithm is demo nstrated by comparing it with the existing parallel algorithm, based o n Cholesky factorization, using extensive simulation studies on two-di mensional problems discretized by FEM.