Analysis of Krylov subspace approximation to large-scale differential Riccati equations

DOI10.1553/etna_vol52s431zbMath1456.65019arXiv1705.07507OpenAlexW3134025662MaRDI QIDQ2218919

Koskela Antti, Hermann Mena

Publication date: 18 January 2021

Published in: ETNA. Electronic Transactions on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1705.07507

zbMATH Keywords

ordinary differential equationsKrylov subspace methodslow-rank approximationoptimal control problemsmodel order reductionexponential integratorsdifferential Riccati equations

Mathematics Subject Classification ID

Linear systems in control theory (93C05) Iterative numerical methods for linear systems (65F10) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Large-scale systems (93A15) Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs (65M22) Numerical computation of matrix exponential and similar matrix functions (65F60) Numerical methods for matrix equations (65F45)

Related Items (4)

Positivity preserving exponential integrators for differential Riccati equations ⋮ Low-rank parareal: a low-rank parallel-in-time integrator ⋮ GPU acceleration of splitting schemes applied to differential matrix equations ⋮ Solving differential Riccati equations: a nonlinear space-time method using tensor trains

Cites Work

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• Minimal residual methods for large scale Lyapunov equations
• Preserving geometric properties of the exponential matrix by block Krylov subspace methods
• Positive definiteness in the numerical solution of Riccati differential equations
• Matrix Riccati equations in control and systems theory
• Adaptive high-order splitting schemes for large-scale differential Riccati equations
• Numerical solution of the infinite-dimensional LQR problem and the associated Riccati differential equations
• Preserving monotonicity in the numerical solution of Riccati differential equations
• Structure preserving integrators for solving (non-)linear quadratic optimal control problems with applications to describe the flight of a quadrotor
• On the benefits of the \(L D L^T\) factorization for large-scale differential matrix equation solvers
• Analysis of the Rational Krylov Subspace Projection Method for Large-Scale Algebraic Riccati Equations
• Residual, Restarting, and Richardson Iteration for the Matrix Exponential
• Rational Krylov approximation of matrix functions: Numerical methods and optimal pole selection
• Exponential integrators
• Low-Rank Second-Order Splitting of Large-Scale Differential Riccati Equations
• On Adaptive Choice of Shifts in Rational Krylov Subspace Reduction of Evolutionary Problems
• Error Estimates and Evaluation of Matrix Functions via the Faber Transform
• A new investigation of the extended Krylov subspace method for matrix function evaluations
• A New Iterative Method for Solving Large-Scale Lyapunov Matrix Equations
• Numerical integration of the differential matrix Riccati equation
• A Schur method for solving algebraic Riccati equations
• Analysis of Some Krylov Subspace Approximations to the Matrix Exponential Operator
• Efficient Solution of Parabolic Equations by Krylov Approximation Methods
• On Krylov Subspace Approximations to the Matrix Exponential Operator
• Low-rank approximate solutions to large-scale differential matrix Riccati equations
• The Scaling and Squaring Method for the Matrix Exponential Revisited
• Rosenbrock Methods for Solving Riccati Differential Equations
• Functions of Matrices
• The numerical solution of the matrix Riccati differential equation

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