Superfast Inversion of Two-Level Toeplitz Matrices Using Newton Iteration and Tensor-Displacement Structure

Abstract

A fast approximate inversion algorithm is proposed for two-level Toeplitz matrices (block Toeplitz matrices with Toeplitz blocks). It applies to matrices that can be sufficiently accurately approximated by matrices of low Kronecker rank and involves a new class of tensor-displacement-rank structured (TDS) matrices. The complexity depends on the prescribed accuracy and typically is o(n) for matrices of order n.