Efficient factorization and solution algorithms on vector computers

Abstract

Soon after their appearance, large vector computers were tested for the solution of power system problems such as security analysis and transient stability. The first results were discouraging, mainly because the consolidated sparsity exploiting algorithms performed poorly on vector computers, which are designed to work at their peak performance when operating with long full vectors. In this paper, the operations needed to perform factorization and solution of sparse sets of linear equations are rearranged in the form of long Fortran DO loops. The main result achieved by the proposed method is that faster factorization and solution algorithms are obtained by changing only the order of operations, without altering the operation count of the standard sparsity based algorithm. Tests on CRAY Y-MP8/432 and on IBM 3090/200S VF vector computers demonstrate the effectiveness of the proposed approach in comparison with the standard factorization and solution algorithms.