Latest Inversion-Free Iterative Scheme for Solving a Pair of Nonlinear Matrix Equations
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In this work, the following system of nonlinear matrix equations is considered, X 1 + A ∗ X 1 − 1 A + B ∗ X 2 − 1 B = I and X 2 + C ∗ X 2 − 1 C + D ∗ X 1 − 1 D = I , where A , B , C , and D are arbitrary n × n matrices and I is the identity matrix of order n . Some conditions for the existence of a positive-definite solution as well as the convergence analysis of the newly developed algorithm for finding the maximal positive-definite solution and its convergence rate are discussed. Four examples are also provided herein to support our results.
2019 ◽
Vol 9
(2)
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pp. 526-546
2017 ◽
Vol 66
(4)
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pp. 827-839
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2007 ◽
Vol 14
(2)
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pp. 99-113
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2012 ◽
Vol 450-451
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pp. 158-161