Low-rank updates and divide-and-conquer methods for quadratic matrix equations

DOI10.1007/s11075-019-00776-wOpenAlexW2963353225MaRDI QIDQ2181678

Patrick Kürschner, Stefano Massei, Daniel Kressner

Publication date: 19 May 2020

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1903.02343

zbMATH Keywords

Riccati equationhierarchical matricesdivide-and-conquerlow-rank updateunilateral quadratic matrix equation

Mathematics Subject Classification ID

Numerical analysis (65-XX)

Related Items (2)

A Numerical Comparison of Different Solvers for Large-Scale, Continuous-Time Algebraic Riccati Equations and LQR Problems ⋮ Numerical computation and new output bounds for time-limited balanced truncation of discrete-time systems

Uses Software

• CAREX
• RKToolbox
• GitHub
• Hm-toolbox
• RADI

Cites Work

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• Adaptive rational Krylov subspaces for large-scale dynamical systems
• Solution of large scale algebraic matrix Riccati equations by use of hierarchical matrices
• On the decay of the off-diagonal singular values in cyclic reduction
• Extended Arnoldi methods for large low-rank Sylvester matrix equations
• RADI: a low-rank ADI-type algorithm for large scale algebraic Riccati equations
• Factorized solution of Lyapunov equations based on hierarchical matrix arithmetic
• A robust numerical method for the \(\gamma\)-iteration in \(H_{\infty}\) control
• The cyclic reduction algorithm: From Poisson equation to stochastic processes and beyond. In memoriam of Gene H. Golub
• Near-circularity for the rational Zolotarev problem in the complex plane
• The rational Krylov algorithm for nonsymmetric eigenvalue problems. III: Complex shifts for real matrices
• A structure-preserving doubling algorithm for continuous-time algebraic Riccati equations
• Backward error and condition of polynomial eigenvalue problems
• On the benefits of the \(L D L^T\) factorization for large-scale differential matrix equation solvers
• Efficient cyclic reduction for quasi-birth-death problems with rank structured blocks
• An \(\mathcal O(N\log N)\) fast direct solver for partial hierarchically semi-separable matrices. With application to radial basis function interpolation
• Non-negative matrices and Markov chains.
• A structure-preserving doubling algorithm for nonsymmetric algebraic Riccati equation
• Generalization and variations of Pellet's theorem for matrix polynomials
• Analysis of the Rational Krylov Subspace Projection Method for Large-Scale Algebraic Riccati Equations
• A Compressed Cyclic Reduction for QBD processes with Low-Rank Upper and Lower Transitions
• Numerical solution of large and sparse continuous time algebraic matrix Riccati and Lyapunov equations: a state of the art survey
• Hierarchical Matrices: Algorithms and Analysis
• Error Estimates and Evaluation of Matrix Functions via the Faber Transform
• Numerical Solution of Algebraic Riccati Equations
• Tail Decay Rates in Double QBD Processes and Related Reflected Random Walks
• A New Iterative Method for Solving Large-Scale Lyapunov Matrix Equations
• Numerical solution of large‐scale Lyapunov equations, Riccati equations, and linear‐quadratic optimal control problems
• Detecting and Solving Hyperbolic Quadratic Eigenvalue Problems
• Defect correction method for the solution of algebraic Riccati equations
• Introduction to Matrix Analytic Methods in Stochastic Modeling
• Rational Krylov: A Practical Algorithm for Large Sparse Nonsymmetric Matrix Pencils
• Numerical analysis of a quadratic matrix equation
• On the Singular Values of Matrices with Displacement Structure
• Low-Rank Updates and a Divide-And-Conquer Method for Linear Matrix Equations
• hm-toolbox: MATLAB Software for HODLR and HSS Matrices
• A Numerical Comparison of Different Solvers for Large-Scale, Continuous-Time Algebraic Riccati Equations and LQR Problems
• Numerical Algebra, Matrix Theory, Differential-Algebraic Equations and Control Theory
• Numerical Methods for Structured Markov Chains
• On two numerical methods for the solution of large-scale algebraic Riccati equations

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