Fixed point iterative methods for solving the nonlinear matrix equation \(X-A^*X^{-n}A=I\)

DOI10.1007/s12190-022-01806-yzbMath1522.15017OpenAlexW4307804914MaRDI QIDQ6138313

Publication date: 5 September 2023

Published in: Journal of Applied Mathematics and Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12190-022-01806-y

zbMATH Keywords

Fréchet derivative nonlinear matrix equation fixed point iteration Hermitian positive definite solution

Mathematics Subject Classification ID

Fixed-point theorems (47H10) Matrix equations and identities (15A24) Numerical methods for matrix equations (65F45)

Cites Work

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Ladder networks, fixpoints, and the geometric mean
Schur complements and statistics
Functional calculus for sesquilinear forms and the purification map
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A novel iterative method for the solution of a nonlinear matrix equation
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Stabilizability of Linear Systems Over a Commutative Normed Algebra with Applications to Spatially-Distributed and Parameter-Dependent Systems
Iterative solution of two matrix equations
Computing the Extremal Positive Definite Solutions of a Matrix Equation
Consistent Estimates of the Parameters of a Linear System
On Direct Methods for Solving Poisson’s Equations
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Two iteration processes for computing positive definite solutions of the equation \(X-A^*X^{-n}A=Q\)

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