On a family of low-rank algorithms for large-scale algebraic Riccati equations

DOI10.1016/j.laa.2024.01.020arXiv2304.01624WikidataQ128775724 ScholiaQ128775724MaRDI QIDQ6118776

Heike Fassbender, Christian Bertram

Publication date: 28 February 2024

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

Full work available at URL: https://arxiv.org/abs/2304.01624

zbMATH Keywords

algebraic Riccati equationADI iteration(block) rational Krylov subspacelarge-scale matrix equation

Mathematics Subject Classification ID

Numerical methods for matrix equations (65F45)

Cites Work

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• An invariant subspace method for large-scale algebraic Riccati equation
• 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
• Rational Krylov sequence methods for eigenvalue computation
• 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
• Rational Krylov for real pencils with complex eigenvalues
• Rational Krylov algorithms for nonsymmetric eigenvalue problems. II: Matrix pairs
• Efficient handling of complex shift parameters in the low-rank Cholesky factor ADI method
• The ADI iteration for Lyapunov equations implicitly performsH2pseudo-optimal model order reduction
• Analysis of an Iteration Method for the Algebraic Riccati Equation
• Analysis of the Rational Krylov Subspace Projection Method for Large-Scale Algebraic Riccati Equations
• Numerical solution of large and sparse continuous time algebraic matrix Riccati and Lyapunov equations: a state of the art survey
• An improved numerical method for balanced truncation for symmetric second-order systems
• A new subspace iteration method for the algebraic Riccati equation
• The university of Florida sparse matrix collection
• Rational Krylov: A Practical Algorithm for Large Sparse Nonsymmetric Matrix Pencils
• A Cyclic Low-Rank Smith Method for Large Sparse Lyapunov Equations
• Low Rank Solution of Lyapunov Equations
• A Numerical Comparison of Different Solvers for Large-Scale, Continuous-Time Algebraic Riccati Equations and LQR Problems
• The Block Rational Arnoldi Method
• Approximate residual-minimizing shift parameters for the low-rank ADI iteration
• Generalized Rational Krylov Decompositions with an Application to Rational Approximation
• On two numerical methods for the solution of large-scale algebraic Riccati equations