Connection Machine implementation of an appropriate inverse preconditioning with minimum residual iteration

A discussion is presented of the implementation on the Connection Machine (CM) of a minimum residual-type iterative method with approximate inverse matrix preconditioning for solving large, sparse, square, nonsymmetric matrices. Computing the approximate inverse in the Frobenius norm decouples into a collection of least squares subproblems for the determination of the columns. This computation is parallelized on the CM by configuring its processors into a three-dimensional array and assigning to each slice of the array a particular least squares submatrix. The solutions of the least squares subproblems are then gathered into a form appropriate for matrix-vector multiplication. Application of the residual algorithm reduces to a series of matrix-vector and vector-vector operations, all highly parallelized on the CM