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arXiv · 1407.0671

Optimal rates of convergence of matrices with applications

Heinz H. Bauschke·J. Y. Bello Cruz·Tran T. A. Nghia·Hung M. Phan·Xianfu Wang
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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.

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Heinz H. Bauschke, J. Y. Bello Cruz, Tran T. A. Nghia, Hung M. Phan, Xianfu Wang. 2014-07-02. Optimal rates of convergence of matrices with applications. https://arxiv.org/abs/1407.0671

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