ADI preconditioned Krylov methods for large Lyapunov matrix equations
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Publication:962079
DOI10.1016/j.laa.2009.12.025zbMath1189.65078OpenAlexW2008567148MaRDI QIDQ962079
Publication date: 6 April 2010
Published in: Linear Algebra and its Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.laa.2009.12.025
convergencenumerical examplespreconditioningLyapunov matrix equationglobal Arnoldi methodStein matrix equationlow-rank approximationsADImatrix Krylov subspace methodalternating direction implicit iteration method
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Cites Work
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- Solution of Lyapunov equations by alternating direction implicit iteration
- On the ADI method for Sylvester equations
- Iterative solution of the Lyapunov matrix equation
- Krylov-subspace methods for the Sylvester equation
- Solving stable generalized Lyapunov equations with the matrix sign function
- Eigenvalue decay bounds for solutions of Lyapunov equations: the symmetric case
- Global FOM and GMRES algorithms for matrix equations
- Projection methods for large Lyapunov matrix equations
- Low rank approximate solutions to large Sylvester matrix equations
- Convergence properties of some block Krylov subspace methods for multiple linear systems
- Balanced Truncation Model Reduction of Large-Scale Dense Systems on Parallel Computers
- Efficient numerical solution of the LQR-problem for the heat equation
- The Numerical Solution of Parabolic and Elliptic Differential Equations
- A New Iterative Method for Solving Large-Scale Lyapunov Matrix Equations
- Numerical solution of large‐scale Lyapunov equations, Riccati equations, and linear‐quadratic optimal control problems
- Direct methods and ADI‐preconditioned Krylov subspace methods for generalized Lyapunov equations
- GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
- A Hessenberg-Schur method for the problem AX + XB= C
- A Characterization of All Solutions to the Four Block General Distance Problem
- A numerical algorithm to solve<tex>A^{T}XA - X = Q</tex>
- Krylov Subspace Methods for Solving Large Lyapunov Equations
- Preconditioned Krylov Subspace Methods for Lyapunov Matrix Equations
- A Cyclic Low-Rank Smith Method for Large Sparse Lyapunov Equations
- Low Rank Solution of Lyapunov Equations
- Algorithm 432 [C2: Solution of the matrix equation AX + XB = C [F4]]
- Matrix Equation $XA + BX = C$
- Extended Application of Alternating Direction Implicit Iteration Model Problem Theory
