On global Hessenberg based methods for solving Sylvester matrix equations

DOI10.1016/j.camwa.2018.09.015zbMath1442.65064OpenAlexW2899843038WikidataQ128981513 ScholiaQ128981513MaRDI QIDQ2203712

Farid Saberi-Movahed, Azita Tajaddini, Mohammed Heyouni

Publication date: 2 October 2020

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2018.09.015

zbMATH Keywords

preconditioningSylvester matrix equationSylvester global CMRH methodSylvester global generalized Hessenberg processSylvester global GMRES method

Mathematics Subject Classification ID

Matrix equations and identities (15A24) Numerical methods for matrix equations (65F45)

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Uses Software

• CMRH
• MatrixMarket

Cites Work

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• A new look at CMRH and its relation to GMRES
• A minimal residual norm method for large-scale Sylvester matrix equations
• Extended Arnoldi methods for large low-rank Sylvester matrix equations
• Matrix Krylov subspace methods for large scale model reduction problems
• Model reduction in large scale MIMO dynamical systems via the block Lanczos method
• On a variable smoothing procedure for Krylov subspace methods
• Alternating direction method for generalized Sylvester matrix equation \(AXB + CYD = E\)
• A matrix CRS iterative method for solving a class of coupled Sylvester-transpose matrix equations
• Restarted Hessenberg method for solving shifted nonsymmetric linear systems
• On the least squares generalized Hamiltonian solution of generalized coupled Sylvester-conjugate matrix equations
• CMRH: A new method for solving nonsymmetric linear systems based on the Hessenberg reduction algorithm
• Global FOM and GMRES algorithms for matrix equations
• Preconditioning techniques for large linear systems: A survey
• A theoretical overview of Krylov subspace methods
• An iterative algorithm for the least Frobenius norm least squares solution of a class of generalized coupled Sylvester-transpose linear matrix equations
• Flexible global generalized Hessenberg methods for linear systems with multiple right-hand sides
• A note on the numerical approximate solutions for generalized Sylvester matrix equations with applications
• A new implementation of the CMRH method for solving dense linear systems
• Low rank approximate solutions to large Sylvester matrix equations
• Matrix Krylov subspace methods for linear systems with multiple right-hand sides
• Computational Methods for Linear Matrix Equations
• Recent computational developments in Krylov subspace methods for linear systems
• Krylov Subspace Methods on Supercomputers
• The Lanczos and Conjugate Gradient Algorithms
• FQMR: A Flexible Quasi-Minimal Residual Method with Inexact Preconditioning
• The global Hessenberg and CMRH methods for linear systems with multiple right-hand sides