Parallel algorithm and architectures for two-step division-free Gaussian elimination

The design of optimal array processors for solving linear systems using two-step division-free Gaussian elimination method is considered. The two-step method circumvents the one-step one in terms of numerical stability. In spite of the rather complicated computations needed at each iteration of the two-step method, we develop an innovative parallel algorithm whose data dependency graph meets the requirements for regularity and locality. Then we derive two-dimensional array processors by adopting a systematic approach to investigate the set of all admissible solutions and obtain the optimal array processors under linear time-space scheduling. The array processors is optimal in terms of the number of processing elements used.