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On the Hermitian positive defnite solution of the nonlinear matrix equation X + A*X −1 A + B*X −1 B = I

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Abstract

In this paper, we study the matrix equation X + A*X −1 A + B*X −1 B = I, where A, B are square matrices, and obtain some conditions for the existence of the positive definite solution of this equation. Two iterative algorithms to find the positive definite solution are given. Some numerical results are reported to illustrate the effectiveness of the algorithms.

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Authors and Affiliations

  1. College of Mathematics, Changsha, 410082, China

    Jian-hui Long

  2. Department of Mathematics and Physics, Fujian University of Technology, Fuzhou, 350014, China

    Jian-hui Long

  3. College of Mathematics and Econometrics, Hunan University, Changsha, 410082, China

    Xi-yan Hu & Lei Zhang

Authors
  1. Jian-hui Long
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  2. Xi-yan Hu
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  3. Lei Zhang
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Correspondence to Jian-hui Long.

Additional information

This research supported by the National Natural Science Foundation of China 10571047 and Doctorate Foundation of the Ministry of Education of China 20060532014.

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Long, Jh., Hu, Xy. & Zhang, L. On the Hermitian positive defnite solution of the nonlinear matrix equation X + A*X −1 A + B*X −1 B = I . Bull Braz Math Soc, New Series 39, 371–386 (2008). https://doi.org/10.1007/s00574-008-0011-7

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  • DOI: https://doi.org/10.1007/s00574-008-0011-7

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