Nonlinear Least-Squares Approach for Large-Scale Algebraic Riccati Equations

DOI10.1137/18M1198922zbMath1420.65035OpenAlexW2957175436WikidataQ127476311 ScholiaQ127476311MaRDI QIDQ5230649

Marcos Raydan, Khalide Jbilou

Publication date: 28 August 2019

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/18m1198922

zbMATH Keywords

Gauss-Newton methodrational Krylov subspacesextended block Arnoldi subspacesGalerkin-projection methodsglobal conjugate gradient methodlarge-scale Riccati equations

Mathematics Subject Classification ID

Uses Software

• RICPAC
• RADI

Cites Work

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• Adaptive rational Krylov subspaces for large-scale dynamical systems
• Minimal residual methods for large scale Lyapunov equations
• RADI: a low-rank ADI-type algorithm for large scale algebraic Riccati equations
• An inexact low-rank Newton-ADI method for large-scale algebraic Riccati equations
• An extended block Arnoldi algorithm for large-scale solutions of the continuous-time algebraic Riccati equation
• On the solution of large-scale algebraic Riccati equations by using low-dimensional invariant subspaces
• Linear dynamical systems. A rev. ed. of ``Dynamical systems and their applications: linear theory
• Dykstra's algorithm for constrained least-squares rectangular matrix problems
• The Riccati equation
• The autonomous linear quadratic control problem. Theory and numerical solution
• Matrix Riccati equations in control and systems theory
• Block Krylov subspace methods for large algebraic Riccati equations
• Global FOM and GMRES algorithms for matrix equations
• Inexact Newton's method with inner implicit preconditioning for algebraic Riccati equations
• An Arnoldi based algorithm for large algebraic Riccati equations
• Analysis of an Iteration Method for the Algebraic Riccati Equation
• Analysis of the Rational Krylov Subspace Projection Method for Large-Scale Algebraic Riccati Equations
• A new subspace iteration method for the algebraic Riccati equation
• State-space solutions to standard H/sub 2/ and H/sub infinity / control problems
• A New Iterative Method for Solving Large-Scale Lyapunov Matrix Equations
• Inexact Kleinman–Newton Method for Riccati Equations
• Numerical solution of large‐scale Lyapunov equations, Riccati equations, and linear‐quadratic optimal control problems
• A Schur method for solving algebraic Riccati equations
• A Generalized Eigenvalue Approach for Solving Riccati Equations
• Linear model reduction and solution of the algebraic Riccati equation by use of the sign function†
• Krylov Subspace Methods for Solving Large Lyapunov Equations
• Extended Krylov Subspaces: Approximation of the Matrix Square Root and Related Functions
• Analysis and modificaton of Newton’s method for algebraic Riccati equations
• A Numerical Comparison of Different Solvers for Large-Scale, Continuous-Time Algebraic Riccati Equations and LQR Problems
• On two numerical methods for the solution of large-scale algebraic Riccati equations
• Matrix theory. Basic results and techniques
• Block Krylov subspace methods for solving large Sylvester equations
• RADI

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