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Some iterative methods for the largest positive definite solution to a class of nonlinear matrix equation

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Abstract

In this paper, we propose some inversion-free iteration methods for finding the largest positive definite solution of a class of nonlinear matrix equation. Then, we consider the properties of the solution for this nonlinear matrix equation. Also, we establish Newton’s iteration method for finding the largest positive definite solution and prove its quadratic convergence. Furthermore, we derive the semi-local convergence of the Newton’s iteration method. Finally, some numerical examples are presented to illustrate the effectiveness of the theoretical results and the behavior of the considered methods.

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Authors and Affiliations

  1. College of Mathematics and Informatics, Fujian Key Laborotary of Mathematical Analysis and Applications, Fujian Normal University, Fuzhou, 350117, People’s Republic of China

    Bao-Hua Huang & Chang-Feng Ma

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  1. Bao-Hua Huang
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  2. Chang-Feng Ma
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Correspondence to Chang-Feng Ma.

Additional information

Supported by Fujian Natural Science Foundation (Grant No. 2016J01005) and Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB18010202).

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Huang, BH., Ma, CF. Some iterative methods for the largest positive definite solution to a class of nonlinear matrix equation. Numer Algor 79, 153–178 (2018). https://doi.org/10.1007/s11075-017-0432-8

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