%0 Journal Article
%T Optimal rates of convergence of matrices with applications
%A Heinz H. Bauschke
%A J. Y. Bello Cruz
%A Tran T. A. Nghia
%A Hung M. Phan
%A Xianfu Wang
%J Mathematics
%D 2014
%I arXiv
%X We present a systematic study on the linear convergence rates of the powers of (real or complex) matrices. We derive a characterization when the optimal convergence rate is attained. This characterization is given in terms of semi-simpleness of all eigenvalues having the second-largest modulus after 1. We also provide applications of our general results to analyze the optimal convergence rates for several relaxed alternating projection methods and the generalized Douglas-Rachford splitting methods for finding the projection on the intersection of two subspaces. Numerical experiments confirm our convergence analysis.
%U http://arxiv.org/abs/1407.0671v1