Fast positive definite linear system solvers

Abstract

The authors show that the M-band wavelet transforms of a wide class of covariance matrices consist of subblocks that are essentially banded. Furthermore, they prove that the Cholesky factors of the transformed covariance matrices also consist of subblocks that are essentially banded. They combine these two observations to construct a fast O(N/sup 2/) algorithm for solving the N/spl times/N linear positive definite systems of equations that arise in statistical signal processing. Finally, they provide an error analysis of the proposed linear positive definite system solver.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>