Solving Parameter-Dependent Lyapunov Equations Using the Reduced Basis Method with Application to Parametric Model Order Reduction
From MaRDI portal
Publication:5270417
DOI10.1137/15M1027097zbMath1367.65066OpenAlexW2620454086MaRDI QIDQ5270417
Nguyen Thanh Son, Tatjana Stykel
Publication date: 23 June 2017
Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/15m1027097
error estimatesnumerical examplesgreedy algorithmreduced basis methodmodel order reductionLyapunov matrix equationsaffine dependencemin-\(\theta\) approachparameter-dependent Lyapunov equationsparametric balanced truncation
Related Items
On the solutions of a class of tensor equations, Reduced basis approximation of large scale parametric algebraic Riccati equations, Optimization-based Parametric Model Order Reduction via ${{\mathcal{H}_2} \otimes {\mathcal{L}_2}}$ First-order Necessary Conditions, Balanced truncation for model reduction of biological oscillators, Greedy algorithm for parameter dependent operator Lyapunov equations, Stability-preserving model order reduction for linear stochastic Galerkin systems, 2 Balancing-related model reduction methods, Stability Preservation in Stochastic Galerkin Projections of Dynamical Systems, Balanced Truncation for Parametric Linear Systems Using Interpolation of Gramians: A Comparison of Algebraic and Geometric Approaches, Parametric Model Order Reduction Using pyMOR, Preconditioned linear solves for parametric model order reduction
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Solution of Lyapunov equations by alternating direction implicit iteration
- Solving the algebraic Riccati equation with the matrix sign function
- Iterative solution of the Lyapunov matrix equation
- Reduced-basis approximation of the viscous Burgers equation: Rigorous a posteriori error bounds.
- A modified low-rank Smith method for large-scale Lyapunov equations
- Perturbation theory and backward error for \(AX - XB = C\)
- The logarithmic norm. History and modern theory
- Lyapunov matrix equations in system stability and control.
- Numerical solution of large and sparse continuous time algebraic matrix Riccati and Lyapunov equations: a state of the art survey
- Certified Reduced Basis Methods for Parametrized Partial Differential Equations
- A preconditioned low-rank CG method for parameter-dependent Lyapunov matrix equations
- Efficient reduced models anda posteriorierror estimation for parametrized dynamical systems by offline/online decomposition
- A Riemannian Optimization Approach for Computing Low-Rank Solutions of Lyapunov Equations
- Analysis of the Rational Krylov Subspace and ADI Methods for Solving the Lyapunov Equation
- Reduced basis approximation of large scale parametric algebraic Riccati equations
- Computational Methods for Linear Matrix Equations
- A New Iterative Method for Solving Large-Scale Lyapunov Matrix Equations
- Matrix Analysis
- Truncated balanced realization of a stable non-minimal state-space system
- Numerical Solution of the Stable, Non-negative Definite Lyapunov Equation Lyapunov Equation
- Krylov Subspace Methods for Solving Large Lyapunov Equations
- Solution of the Sylvester matrix equation AXB T + CXD T = E
- A Cyclic Low-Rank Smith Method for Large Sparse Lyapunov Equations
- Model Reduction and Approximation
- Certified real‐time solution of the parametrized steady incompressible Navier–Stokes equations: rigorous reduced‐basis a posteriori error bounds
- Low Rank Solution of Lyapunov Equations
- A Parametric Lyapunov Equation Approach to the Design of Low Gain Feedback
- Algorithm 432 [C2: Solution of the matrix equation AX + XB = C [F4]]
- Reduced basis method for finite volume approximations of parametrized linear evolution equations
- Reduced Basis Methods for Partial Differential Equations
- Approximation of Large-Scale Dynamical Systems
