Low-rank Newton-ADI methods for large nonsymmetric algebraic Riccati equations
From MaRDI portal
Publication:285684
DOI10.1016/j.jfranklin.2015.04.016zbMath1336.93056OpenAlexW1494550340WikidataQ115214647 ScholiaQ115214647MaRDI QIDQ285684
Jens Saak, Peter Benner, Patrick Kürschner
Publication date: 19 May 2016
Published in: Journal of the Franklin Institute (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jfranklin.2015.04.016
Galerkin projectionacceleration of Newtons schemeadapted shift parameter strategies for FADIlarge nonsymmetric algebraic Riccati equationslow-rank Newton-alternating direction implicit iteration (ADI) methodsnorm of residual matrix
Iterative numerical methods for linear systems (65F10) Control/observation systems governed by ordinary differential equations (93C15) Large-scale systems (93A15)
Related Items
Solving large-scale nonsymmetric algebraic Riccati equations from two-dimensional transport models by doubling ⋮ A Numerical Comparison of Different Solvers for Large-Scale, Continuous-Time Algebraic Riccati Equations and LQR Problems ⋮ Event-triggered zeroing dynamics for motion control of Stewart platform ⋮ Exponential integrators for large-scale stiff Riccati differential equations ⋮ On the solution of the nonsymmetric T-Riccati equation ⋮ Newton's method for the positive solution of the coupled algebraic Riccati equation applied to automatic control ⋮ Structured Shamanskii methods for Chandrasekhar equation arising from radiation ⋮ Matrix Equations, Sparse Solvers: M-M.E.S.S.-2.0.1—Philosophy, Features, and Application for (Parametric) Model Order Reduction ⋮ A class of fixed point iteration for the coupled algebraic Riccati equation
Uses Software
Cites Work
- Unnamed Item
- Solution of a nonsymmetric algebraic Riccati equation from a two-dimensional transport model
- On the numerical solution of large-scale sparse discrete-time Riccati equations
- On the ADI method for Sylvester equations
- Three methods for refining estimates of invariant subspaces
- Iterative solution of the Lyapunov matrix equation
- Total linear least squares and the algebraic Riccati equation
- Matrix Riccati equations in control and systems theory
- Direct methods for matrix Sylvester and Lyapunov equations
- The Riccati algorithm for eigenvalues and invariant subspaces of matrices with inexpensive action
- On the ADI method for the Sylvester equation and the optimal-\({\mathcal H}_{2}\) points
- Self-generating and efficient shift parameters in ADI methods for large Lyapunov and Sylvester equations
- Computing real low-rank solutions of Sylvester equations by the factored ADI method
- Low memory and low complexity iterative schemes for a nonsymmetric algebraic Riccati equation arising from transport theory
- Efficient methods for solving a nonsymmetric algebraic Riccati equation arising in stochastic fluid models
- Low rank approximate solutions to large Sylvester matrix equations
- Solving stable Sylvester equations via rational iterative schemes
- On the Iterative Solution of a Class of Nonsymmetric Algebraic Riccati Equations
- The ADI iteration for Lyapunov equations implicitly performsH2pseudo-optimal model order reduction
- Numerical solution of large and sparse continuous time algebraic matrix Riccati and Lyapunov equations: a state of the art survey
- Solving Large-Scale Nonsymmetric Algebraic Riccati Equations by Doubling
- Krylov Subspace Methods for Linear Systems with Tensor Product Structure
- Numerical Solution of Algebraic Riccati Equations
- The ADI Model Problem
- Inexact Kleinman–Newton Method for Riccati Equations
- Numerical solution of large‐scale Lyapunov equations, Riccati equations, and linear‐quadratic optimal control problems
- A Fast Newton's Method for a Nonsymmetric Algebraic Riccati Equation
- Explicit Solutions for a Riccati Equation from Transport Theory
- A Hessenberg-Schur method for the problem AX + XB= C
- Linear model reduction and solution of the algebraic Riccati equation by use of the sign function†
- Iterative solution for a certain class of algebraic matrix riccati equations arising in transport theory
- Algorithm 432 [C2: Solution of the matrix equation AX + XB = C [F4]]
- A preconditioned block Arnoldi method for large Sylvester matrix equations
- Functions of Matrices
- Iterative Solution of a Nonsymmetric Algebraic Riccati Equation
- Block Krylov subspace methods for solving large Sylvester equations
