The asymptotic analysis of the structure-preserving doubling algorithms

DOI10.1016/j.laa.2017.06.005zbMath1375.65061OpenAlexW2621889325MaRDI QIDQ2402456

Shih-Feng Shieh, Yueh-Cheng Kuo, Wen-Wei Lin

Publication date: 7 September 2017

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2017.06.005

zbMATH Keywords

convergence ratesnonlinear matrix equationsmatrix Riccati differential equationssymplectic pairsHamiltonian Jordan canonical formdiscrete-time algebraicstructure-preserving doubling algorithmsstructure-preserving flows

Mathematics Subject Classification ID

Related Items (2)

The orthogonal flows for orthogonal iteration ⋮ A structure preserving flow for computing Hamiltonian matrix exponential

Cites Work

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• Structured doubling algorithms for weakly stabilizing Hermitian solutions of algebraic Riccati equations
• The autonomous linear quadratic control problem. Theory and numerical solution
• Matrix Riccati equations in control and systems theory
• Convergence and existence results for continuous- and discrete-time Riccati equations
• Necessary and sufficient conditions for the existence of a positive definite solution of the matrix equation \(X+A^*X^{-1}A=Q\)
• Non-symmetric matrix Riccati equations
• Convergence of the time-invariant Riccati differential equation towards its strong solution for stabilizable systems
• A step toward a unified treatment of continuous and discrete time control problems
• Canonical forms for Hamiltonian and symplectic matrices and pencils
• Existence, Uniqueness, and Parametrization of Lagrangian Invariant Subspaces
• Solving a Structured Quadratic Eigenvalue Problem by a Structure-Preserving Doubling Algorithm
• A family of Anadromic numerical methods for matrix Riccati differential equations
• Structure-Preserving Flows of Symplectic Matrix Pairs
• Efficient matrix-valued algorithms for solving stiff Riccati differential equations
• Convergence Analysis of the Doubling Algorithm for Several Nonlinear Matrix Equations in the Critical Case
• Numerical Integration of the Differential Riccati Equation and Some Related Issues
• On the convergence to the strong solution of periodic Riccati equations
• Convergence of the DRE solution to the ARE strong solution
• Doubling Algorithms with Permuted Lagrangian Graph Bases
• Convergence Analysis of Structure-Preserving Doubling Algorithms for Riccati-Type Matrix Equations

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