A monotone geometric mean for a class of Toeplitz matrices

In this paper, using Laurent operators and Fourier coefficients of their symbol functions, we introduce a geometric mean for a large class of n x n positive semi-definite Toeplitz matrices which satisfies the monotonicity property. The cost of our approach in term of arithmetic operations for m matrices is of the order O(mn(2)). This definition preserves the structure, is simple to calculate, preserves monotonicity and satisfies some other Ando Li Mathias properties, (C) 2016 Published by Elsevier Inc.