Structured doubling algorithms for weakly stabilizing Hermitian solutions of algebraic Riccati equations

DOI10.1016/j.laa.2007.08.043zbMath1169.65038OpenAlexW2122055952MaRDI QIDQ1002246

J. Martínez

Publication date: 25 February 2009

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

Full work available at URL: https://doi.org/10.1016/j.laa.2007.08.043

zbMATH Keywords

algorithmsalgebraic Riccati equationnumerical experimentsHermitian solutionunimodular eigenvaluestructured doubling algorithmglobal and linear convergenceHamiltonian and symplectic pencilpurely imaginary eigenvalue

Mathematics Subject Classification ID

Related Items (18)

A new class of complex nonsymmetric algebraic Riccati equations with its ω-comparison matrix being an irreducible singular M-matrix ⋮ Structure-Preserving Flows of Symplectic Matrix Pairs ⋮ The asymptotic analysis of the structure-preserving doubling algorithms ⋮ The structure-preserving doubling algorithm and convergence analysis for a nonlinear matrix equation ⋮ An accelerated technique for solving the positive definite solutions of a class of nonlinear matrix equations ⋮ Structure-Preserving Doubling Algorithms That Avoid Breakdowns for Algebraic Riccati-Type Matrix Equations ⋮ The intrinsic Toeplitz structure and its applications in algebraic Riccati equations ⋮ Doubling algorithm for the discretized Bethe-Salpeter eigenvalue problem ⋮ A generalized structured doubling algorithm for the numerical solution of linear quadratic optimal control problems ⋮ The structure-preserving doubling algorithms for positive definite solution to a system of nonlinear matrix equations ⋮ An iterative method for solving the stable subspace of a matrix pencil and its application ⋮ Two structure-preserving-doubling like algorithms for obtaining the positive definite solution to a class of nonlinear matrix equation ⋮ A structure‐preserving doubling algorithm for Lur'e equations ⋮ A class of complex nonsymmetric algebraic Riccati equations associated with H-matrix ⋮ Optimization of extrapolated Cayley transform with non-Hermitian positive definite matrix ⋮ The double deflating technique for irreducible singular M-matrix algebraic Riccati equations in the critical case ⋮ The convergence analysis of an accelerated iteration for solving algebraic Riccati equations ⋮ A structure preserving flow for computing Hamiltonian matrix exponential

Uses Software

• Matlab
• mctoolbox
• HQR3
• HQR3 EXCHNG

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• On Hamiltonian and symplectic Hessenberg forms
• A numerical method for computing the Hamiltonian Schur form
• A Schur decomposition for Hamiltonian matrices
• Solving the algebraic Riccati equation with the matrix sign function
• A new method for computing the closed-loop eigenvalues of a discrete-time algebraic Riccati equation
• Spectral factorization via Hermitian pencils
• Discrete versions of some classical integrable systems and factorization of matrix polynomials
• The autonomous linear quadratic control problem. Theory and numerical solution
• The matrix sign function and computations in systems
• Parallel algorithm for solving some spectral problems of linear algebra
• An inverse free parallel spectral divide and conquer algorithm for nonsymmetric eigenproblems
• Condition numbers of algebraic Riccati equations in the Frobenius norm
• A structure-preserving doubling algorithm for continuous-time algebraic Riccati equations
• The Moser-Veselov equation
• A step toward a unified treatment of continuous and discrete time control problems
• Canonical forms for Hamiltonian and symplectic matrices and pencils
• A structure-preserving doubling algorithm for nonsymmetric algebraic Riccati equation
• A New Procedure for Stochastic Realization of Spectral Density Matrices
• Hermitian solutions of the discrete algebraic Riccati equation
• A generalization of the matrix-sign-function solution for algebraic Riccati equations
• On Hermitian Solutions of the Symmetric Algebraic Riccati Equation
• Linear Control Theory with an ${\bf H}_\infty $ Optimality Criterion
• Convergence of the doubling algorithm for the discrete-time algebraic Riccati equation
• Doubling algorithm for continuous-time algebraic Riccati equation
• A Schur method for solving algebraic Riccati equations
• Existence and uniqueness theorems for the algebraic Riccati equation
• On the numerical solution of the discrete-time algebraic Riccati equation
• A Generalized Eigenvalue Approach for Solving Riccati Equations
• Accelerated convergence of the matrix sign function method of solving Lyapunov, Riccati and other matrix equations
• A Characterization of All Solutions to the Four Block General Distance Problem
• Two-Riccati formulae for the discrete-time H^∞-control problem
• Second-order convergent algorithms for the steady-state Riccati equation†
• Newton's Method for Discrete Algebraic Riccati Equations when the Closed-Loop Matrix Has Eigenvalues on the Unit Circle
• On Computing Stable Lagrangian Subspaces of Hamiltonian Matrices and Symplectic Pencils
• Perturbation Theory for Algebraic Riccati Equations
• Analysis and modificaton of Newton’s method for algebraic Riccati equations
• Numerical Computation of the Minimal $\mathbfH_\infty$ Norm of the Discrete-Time Output Feedback Control Problem
• Structure-Preserving Algorithms for Periodic Discrete-Time Algebraic Riccati Equations
• Accuracy and Stability of Numerical Algorithms
• Evaluating products of matrix pencils and collapsing matrix products
• Convergence Analysis of Structure-Preserving Doubling Algorithms for Riccati-Type Matrix Equations
• A generalized structure-preserving doubling algorithm for generalized discrete-time algebraic Riccati equations

This page was built for publication: Structured doubling algorithms for weakly stabilizing Hermitian solutions of algebraic Riccati equations