Newton’s Iteration Method for Solving the Nonlinear Matrix Equation <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="bold-italic">X</mi><mo mathvariant="bold">+</mo><msubsup><mo mathvariant="bold">∑</mo><mrow><mi mathvariant="bold-italic">i</mi><mo mathvariant="bold">=</mo><mn mathvariant="bold">1</mn></mrow><mi mathvariant="bold-italic">m</mi></msubsup><msubsup><mi mathvariant="bold-italic">A</mi><mrow><mi mathvariant="bold-italic">i</mi></mrow><mo mathvariant="bold">*</mo></msubsup><msup><mi mathvariant="bold-italic">X</mi><mrow><mo mathvariant="bold">−</mo><mn mathvariant="bold">1</mn></mrow></msup><msub><mi mathvariant="bold-italic">A</mi><mi mathvariant="bold-italic">i</mi></msub><mo mathvariant="bold">=</mo><mi mathvariant="bold-italic">Q</mi></mrow></semantics></math></inline-formula>

In this paper, we study the nonlinear matrix equation (NME) <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>X</mi><mo>+</mo><msubsup><mo>∑</mo><mrow><...

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Bibliographic Details

Main Authors:	Chang-Zhou Li, Chao Yuan, An-Gang Cui
Format:	Article
Language:	English
Published:	MDPI AG 2023-03-01
Series:	Mathematics
Subjects:	nonlinear matrix equation Newton’s iteration method Fr<i>é</i>chet derivative local convergence
Online Access:	https://www.mdpi.com/2227-7390/11/7/1578