Inexact methods for the low rank solution to large scale Lyapunov equations
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Publication:2216489
DOI10.1007/s10543-020-00813-4zbMath1455.65050arXiv1809.06903OpenAlexW3036779051MaRDI QIDQ2216489
Melina A. Freitag, Patrick Kürschner
Publication date: 16 December 2020
Published in: BIT (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1809.06903
Lyapunov equationalternating direction implicit methodlow-rank approximationsrational Krylov subspaces method
Matrix equations and identities (15A24) Numerical methods for low-rank matrix approximation; matrix compression (65F55) Numerical methods for matrix equations (65F45)
Related Items (11)
An efficient, memory-saving approach for the Loewner framework ⋮ A Note on Inexact Inner Products in GMRES ⋮ On an integrated Krylov-ADI solver for large-scale Lyapunov equations ⋮ A Numerical Comparison of Different Solvers for Large-Scale, Continuous-Time Algebraic Riccati Equations and LQR Problems ⋮ Inexact rational Krylov Subspace methods for approximating the action of functions of matrices ⋮ Preconditioned Chebyshev BiCG method for parameterized linear systems ⋮ Relative error-based time-limited \(\mathcal{H}_2\) model order reduction via oblique projection ⋮ Inexact Arnoldi residual estimates and decay properties for functions of non-Hermitian matrices ⋮ Matrix equation techniques for certain evolutionary partial differential equations ⋮ Functions of rational Krylov space matrices and their decay properties ⋮ High order approximations of the operator Lyapunov equation have low rank
Uses Software
Cites Work
- Efficient low-rank solution of generalized Lyapunov equations
- Adaptive rational Krylov subspaces for large-scale dynamical systems
- RADI: a low-rank ADI-type algorithm for large scale algebraic Riccati equations
- Approximating the leading singular triplets of a large matrix function
- An inexact low-rank Newton-ADI method for large-scale algebraic Riccati equations
- Convergence theory for inexact inverse iteration applied to the generalised nonsymmetric eigenproblem
- On the ADI method for Sylvester equations
- The rational Krylov algorithm for nonsymmetric eigenvalue problems. III: Complex shifts for real matrices
- Inexact Rayleigh quotient-type methods for eigenvalue computations
- Efficient handling of complex shift parameters in the low-rank Cholesky factor ADI method
- Self-generating and efficient shift parameters in ADI methods for large Lyapunov and Sylvester equations
- A block MINRES algorithm based on the band Lanczos method
- Computing real low-rank solutions of Sylvester equations by the factored ADI method
- On the decay of the inverse of matrices that are sum of Kronecker products
- Bounds on the trace of a solution to the Lyapunov equation with a general stable matrix
- The ADI iteration for Lyapunov equations implicitly performsH2pseudo-optimal model order reduction
- Analysis of the Rational Krylov Subspace Projection Method for Large-Scale Algebraic Riccati Equations
- Rational Krylov approximation of matrix functions: Numerical methods and optimal pole selection
- Numerical solution of large and sparse continuous time algebraic matrix Riccati and Lyapunov equations: a state of the art survey
- Finite-Rank ADI Iteration for Operator Lyapunov Equations
- An improved numerical method for balanced truncation for symmetric second-order systems
- Analysis of the Rational Krylov Subspace and ADI Methods for Solving the Lyapunov Equation
- The ADI Model Problem
- Computational Methods for Linear Matrix Equations
- A New Iterative Method for Solving Large-Scale Lyapunov Matrix Equations
- Shift-Invert Arnoldi's Method with Preconditioned Iterative Solves
- Using Generalized Cayley Transformations within an Inexact Rational Krylov Sequence Method
- Krylov Subspace Methods for Solving Large Lyapunov Equations
- Theory of Inexact Krylov Subspace Methods and Applications to Scientific Computing
- A Cyclic Low-Rank Smith Method for Large Sparse Lyapunov Equations
- Numerical Methods for Large-Scale Lyapunov Equations with Symmetric Banded Data
- On the Singular Values of Matrices with Displacement Structure
- Low-Rank Updates and a Divide-And-Conquer Method for Linear Matrix Equations
- Inexact Krylov Subspace Methods for Linear Systems
- Low Rank Solution of Lyapunov Equations
- A Numerical Comparison of Different Solvers for Large-Scale, Continuous-Time Algebraic Riccati Equations and LQR Problems
- An Efficient Method for Estimating the Optimal Dampers' Viscosity for Linear Vibrating Systems Using Lyapunov Equation
- Fast Singular Value Decay for Lyapunov Solutions with Nonnormal Coefficients
- Generalized Rational Krylov Decompositions with an Application to Rational Approximation
- Preconditioned Multishift BiCG for $\mathcal{H}_2$-Optimal Model Reduction
- Inexact Matrix-Vector Products in Krylov Methods for Solving Linear Systems: A Relaxation Strategy
- The Numerical Range is a $(1+\sqrt{2})$-Spectral Set
- Two‐stage spectral preconditioners for iterative eigensolvers
- Algorithm 432 [C2: Solution of the matrix equation AX + XB = C [F4]]
- Existence of a low rank or ℋ︁‐matrix approximant to the solution of a Sylvester equation
- On two numerical methods for the solution of large-scale algebraic Riccati equations
- Variable Accuracy of Matrix-Vector Products in Projection Methods for Eigencomputation
- Approximation of Large-Scale Dynamical Systems
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