Analysis of the Rational Krylov Subspace Projection Method for Large-Scale Algebraic Riccati Equations
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Publication:2834694
DOI10.1137/16M1059382MaRDI QIDQ2834694
Publication date: 23 November 2016
Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1602.00649
Variational and other types of inequalities involving nonlinear operators (general) (47J20) Optimal feedback synthesis (49N35) Feedback control (93B52) Numerical methods in optimal control (49M99)
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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
- Minimal residual methods for large scale Lyapunov equations
- An invariant subspace method for large-scale algebraic Riccati equation
- RADI: a low-rank ADI-type algorithm for large scale algebraic Riccati equations
- Error bounds for Newton refinement of solutions to 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
- Rational Krylov for eigenvalue computation and model order reduction
- On the solution of large-scale algebraic Riccati equations by using low-dimensional invariant subspaces
- Model order reduction: Theory, research aspects and applications. Selected papers based on the presentations at the workshop `Model order reduction, coupled problems and optimization', Leiden, The Netherlands, September 19--23, 2005.
- An extended relation between orthogonal rational functions on the unit circle and the interval \([ - 1,1\)]
- Block Krylov subspace methods for large algebraic Riccati equations
- Sylvester equations and projection-based model reduction.
- Dimension reduction of large-scale systems. Proceedings of a workshop, Oberwolfach, Germany, October 19--25, 2003.
- Rational Krylov approximation of matrix functions: Numerical methods and optimal pole selection
- A new subspace iteration method for the algebraic Riccati equation
- On Adaptive Choice of Shifts in Rational Krylov Subspace Reduction of Evolutionary Problems
- On the Convergence of Rational Ritz Values
- Analysis of the Rational Krylov Subspace and ADI Methods for Solving the Lyapunov Equation
- An Error Analysis for Rational Galerkin Projection Applied to the Sylvester Equation
- Numerical Solution of Algebraic Riccati Equations
- Solution of Large Scale Evolutionary Problems Using Rational Krylov Subspaces with Optimized Shifts
- Interpolatory Model Reduction of Large-Scale Dynamical Systems
- Computational Methods for Linear Matrix Equations
- Computable Bounds for the Sensitivity of the Algebraic Riccati Equation
- Lower bounds for separable approximations of the Hilbert kernel
- Inexact Kleinman–Newton Method for Riccati Equations
- Numerical solution of large‐scale Lyapunov equations, Riccati equations, and linear‐quadratic optimal control problems
- Nonlinear multigrid for the solution of large‐scale Riccati equations in low‐rank and ℋ︁‐matrix format
- The Sensitivity of the Stable Lyapunov Equation
- A Cyclic Low-Rank Smith Method for Large Sparse Lyapunov Equations
- An Error Analysis of Galerkin Projection Methods for Linear Systems with Tensor Product Structure
- On two numerical methods for the solution of large-scale algebraic Riccati equations
- Approximation of Large-Scale Dynamical Systems
