Parallel Solution of Toeplitz and Toeplitz-Like Linear Systems Over Fields of Small Positive Characteristic

We show that over a field of characteristic p the solution to a non-singular system of n linear equations in n unknows, with 2 ≤ p < n, whose coefficient matrix is of displacement rank α and which is given as a sum of α LU-products of Toeplitz matrices, can be computed in parallel with randomization simultaneously in O((log n)) time and a total work of O(max{αn, p}n× log n loglog n). A time unit represents an arithmetic operation in the coefficient field. Our solution is based on our recursive parallel triangulation technique for processor-efficient parallel linear system solving over fields of characteristic p. In particular, we show that our recursive parallel triangulation technique can be implemented in a way that preserves Toeplitz-likeness.