Concurrent iterative algorithm for Toeplitz-like linear systems
Victor Ya. Pan · IEEE Transactions on Parallel and Distributed Systems · 1993
A nonsingular n*n matrix A is given with its short displacement generator. It has small displacement rank bounded by a fixed constant. The class of such matrices generalizes Toeplitz matrices. A good initial approximation to a short displacement generator for A/sup -1/ is readily available. Ways to refine this approximation and numerically compute a displacement generator of A/sup -1/ and the solution vector x=A/sup -1/b to a linear system Ax=b by using O(log/sup 2/n) parallel arithmetic steps and n processors are presented. These results are extended to some other important classes of dense structure matrices.>