A preconditioned block Arnoldi method for large Sylvester matrix equations

DOI10.1002/nla.831zbMath1289.65099OpenAlexW2115779696MaRDI QIDQ5397313

M. Hached, Mohammed Heyouni, Abderrahman Bouhamidi, Khalide Jbilou

Publication date: 19 February 2014

Published in: Numerical Linear Algebra with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/nla.831

zbMATH Keywords

numerical exampleconvergence accelerationpreconditionerblock Arnoldi algorithmSylvester matrix equationsalternating direction implicit (ADI)block Krylov methodsnonsymmetric Stein equation

Mathematics Subject Classification ID

Matrix equations and identities (15A24) Iterative numerical methods for linear systems (65F10) Preconditioners for iterative methods (65F08)

Related Items

On some extended block Krylov based methods for large scale nonsymmetric Stein matrix equations, A preconditioned block Arnoldi method for large scale Lyapunov and algebraic Riccati equations, Low-rank Newton-ADI methods for large nonsymmetric algebraic Riccati equations, Computing real low-rank solutions of Sylvester equations by the factored ADI method, On circulant and skew-circulant splitting algorithms for (continuous) Sylvester equations, The constant solution method for solving large-scale differential Sylvester matrix equations with time invariant coefficients, An alternative extended block Arnoldi method for solving low-rank Sylvester equations, A note on the Davison-Man method for Sylvester matrix equations, On some Krylov subspace based methods for large-scale nonsymmetric algebraic Riccati problems, A global variant of the COCR method for the complex symmetric Sylvester matrix equation \(AX+XB=C\)

Uses Software

• LYAPACK
• Algorithm 432

Cites Work

• 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
• Block Krylov subspace methods for large algebraic Riccati equations
• Low rank approximate solutions to large Sylvester matrix equations
• The Numerical Solution of Parabolic and Elliptic Differential Equations
• Matrix Analysis
• A Hessenberg-Schur method for the problem AX + XB= C
• A Characterization of All Solutions to the Four Block General Distance Problem
• Improving the Efficiency of Matrix Operations in the Numerical Solution of Stiff Ordinary Differential Equations
• Krylov Subspace Methods for Solving Large Lyapunov Equations
• A Cyclic Low-Rank Smith Method for Large Sparse Lyapunov Equations
• Low Rank Solution of Lyapunov Equations
• Application of ADI Iterative Methods to the Restoration of Noisy Images
• Algorithm 432 [C2: Solution of the matrix equation AX + XB = C [F4]]
• Matrix Equation $XA + BX = C$
• Block Krylov subspace methods for solving large Sylvester equations