Concurrent iterative algorithm for Toeplitz-like linear systems

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^-1 is readily available. Ways to refine this approximation and numerically compute a displacement generator of A^-1 and the solution vector x= A^-1b to a linear system Ax=b by using O(log²n) parallel arithmetic steps and n processors are presented. These results are extended to some other important classes of dense structure matrices