The block Hessenberg process for matrix equations

zbMath1392.65041MaRDI QIDQ1744302

Mohammed Heyouni, Mohamed Addam, Hassane Sadok

Publication date: 23 April 2018

Published in: ETNA. Electronic Transactions on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: http://etna.mcs.kent.edu/volumes/2011-2020/vol46/abstract.php?vol=46&pages=460-473

zbMATH Keywords

GMRESblock Krylov subspace methodsArnoldi processHessenberg processCMRHlow-rank matrix equations

Mathematics Subject Classification ID

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

Related Items

Block GPBi-CG method for solving nonsymmetric linear systems with multiple right-hand sides and its convergence analysis ⋮ Weighted and flexible versions of block CMRH method for solving nonsymmetric linear systems with multiple right-hand sides ⋮ An alternative extended block Arnoldi method for solving low-rank Sylvester equations ⋮ On Hessenberg type methods for low-rank Lyapunov matrix equations ⋮ On global iterative schemes based on Hessenberg process for (ill-posed) Sylvester tensor equations ⋮ The simpler block CMRH method for linear systems ⋮ Projection schemes based on Hessenberg process for Sylvester tensor equation with low-rank right-hand side ⋮ A Hessenberg-type algorithm for computing PageRank problems

Uses Software

• CMRH

Cites Work

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• A new look at CMRH and its relation to GMRES
• CMRH method as iterative solver for boundary element acoustic systems
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• Algebraic properties of the block GMRES and block Arnoldi methods
• The block conjugate gradient algorithm and related methods
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• The global Hessenberg and CMRH methods for linear systems with multiple right-hand sides
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• Algorithms for the CMRH method for dense linear systems

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