Journal
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
Volume 354, Issue 15, Pages 7088-7118Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.jfranklin.2017.08.018
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Funding
- Ministry of Science and Technology
- National Center for Theoretical Sciences in Taiwan
- Ministry of Science and Technology of Taiwan [MOST 105-2115-M-150-001]
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Nonlinear matrix equations (NMEs) are encountered in many applications of control and engineering problems. In this work, we establish a complete study for a class of nonlinear matrix equations. With the aid of Sherman Morrison Woodbury formula, we have shown that any equation in this class has the maximal positive definite solution under certain conditions. Furthermore, a thorough study of properties about this class of matrix equations is provided. An acceleration of iterative method with R-superlinear convergence is then designed to solve the maximal positive definite solution. Two numerical experiments demonstrate that our methods perform efficiently and reliably. (C) 2017 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.
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