Optimal rates of convergence of matrices with applications
Optimization and Control
2014-07-03 v1 Numerical Analysis
Abstract
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.
Keywords
Cite
@article{arxiv.1407.0671,
title = {Optimal rates of convergence of matrices with applications},
author = {Heinz H. Bauschke and J. Y. Bello Cruz and Tran T. A. Nghia and Hung M. Phan and Xianfu Wang},
journal= {arXiv preprint arXiv:1407.0671},
year = {2014}
}
Comments
32 pages, 3 figures