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The Hermitian Positive Definite Solution of the Nonlinear Matrix Equation

  • Xindong Zhang EMAIL logo und Xinlong Feng
Veröffentlicht/Copyright: 9. Mai 2017
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Abstract:

In this paper, we study the nonlinear matrix equation Xs±i=1mAiTXδiAi=Q, where Ai(i=1,2,,m) is n×n nonsingular real matrix and Q is n×n Hermitian positive definite matrix. It is shown that the equation has an unique Hermitian positive definite solution under some conditions. Iterative algorithms for obtaining the Hermitian positive definite solution of the equation are proposed. Finally, numerical examples are reported to illustrate the effectiveness of algorithms.

MSC 2010: 15B48; 15B57

Acknowledgements:

The research of Xindong Zhang was supported in part by grants NSFC (No.11461072) and the Youth Science and Technology Education Project of Xinjiang (No.QN2016JQ0367).

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Received: 2016-1-24
Accepted: 2017-3-1
Published Online: 2017-5-9
Published in Print: 2017-7-26

© 2017 Walter de Gruyter GmbH, Berlin/Boston

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