On an integrated Krylov-ADI solver for large-scale Lyapunov equations

DOI10.1007/s11075-022-01409-5OpenAlexW4303444660WikidataQ115214626 ScholiaQ115214626MaRDI QIDQ2679651

Davide Palitta, Peter Benner, Jens Saak

Publication date: 23 January 2023

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2203.17174

zbMATH Keywords

Lyapunov equationsshifted linear systemsextended Krylov methodlow-rank ADI

Mathematics Subject Classification ID

Uses Software

• Matlab
• MESS

Cites Work

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• Matrix-equation-based strategies for convection-diffusion equations
• Updating incomplete factorization preconditioners for model order reduction
• Two recursive GMRES-type methods for shifted linear systems with general preconditioning
• RADI: a low-rank ADI-type algorithm for large scale algebraic Riccati equations
• Arnoldi methods for large Sylvester-like observer matrix equations, and an associated algorithm for partial spectrum assignment
• On the parameter selection problem in the Newton-ADI iteration for large-scale Riccati equations
• Extended Krylov subspace for parameter dependent systems
• On the ADI method for Sylvester equations
• The block conjugate gradient algorithm and related methods
• Numerical solution of generalized Lyapunov equations
• Approximate inverse preconditioning for shifted linear systems
• Restarted full orthogonalization method for shifted linear systems
• Eigenvalue decay bounds for solutions of Lyapunov equations: the symmetric case
• Efficient preconditioning for sequences of parametric complex symmetric linear systems
• Iterative system solvers for the frequency analysis of linear mechanical systems
• Efficient handling of complex shift parameters in the low-rank Cholesky factor ADI method
• Inexact methods for the low rank solution to large scale Lyapunov equations
• Self-generating and efficient shift parameters in ADI methods for large Lyapunov and Sylvester equations
• On the benefits of the \(L D L^T\) factorization for large-scale differential matrix equation solvers
• Efficient preconditioner updates for unsymmetric shifted linear systems
• Block Krylov subspace methods for functions of matrices
• Krylov subspace recycling for sequences of shifted linear systems
• Dimension reduction of large-scale systems. Proceedings of a workshop, Oberwolfach, Germany, October 19--25, 2003.
• Frequency-Limited Balanced Truncation with Low-Rank Approximations
• 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
• Subspace recycling accelerates the parametric macro-modeling of MEMS
• Efficient Preconditioner Updates for Shifted Linear Systems
• Analysis of the Rational Krylov Subspace and ADI Methods for Solving the Lyapunov Equation
• The ADI Model Problem
• Recycling BiCG with an Application to Model Reduction
• Computational Methods for Linear Matrix Equations
• Nested Krylov Methods for Shifted Linear Systems
• Numerical linear algebra aspects of control design computations
• Recycling BiCGSTAB with an Application to Parametric Model Order Reduction
• A New Iterative Method for Solving Large-Scale Lyapunov Matrix Equations
• Recycling Krylov Subspaces for Sequences of Linear Systems
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• Optimal Alternating Direction Implicit Parameters for Nonsymmetric Systems of Linear Equations
• Extended Krylov Subspaces: Approximation of the Matrix Square Root and Related Functions
• Restarted GMRES for Shifted Linear Systems
• The Solution of Parametrized Symmetric Linear Systems
• A Krylov Subspace Method for Quadratic Matrix Polynomials with Application to Constrained Least Squares Problems
• A Cyclic Low-Rank Smith Method for Large Sparse Lyapunov Equations
• Low Rank Solution of Lyapunov Equations
• On inexact alternating direction implicit iteration for continuous Sylvester equations
• Approximate residual-minimizing shift parameters for the low-rank ADI iteration
• Fast Singular Value Decay for Lyapunov Solutions with Nonnormal Coefficients
• 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
• Approximation of Large-Scale Dynamical Systems
• Compress‐and‐restart block Krylov subspace methods for Sylvester matrix equations

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