A parallel implementation of the CMRH method for dense linear systems

DOI10.1007/s11075-012-9616-4zbMath1267.65036OpenAlexW2032899988MaRDI QIDQ1952302

Sébastien Duminil

Publication date: 30 May 2013

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

Full work available at URL: https://doi.org/10.1007/s11075-012-9616-4

zbMATH Keywords

linear systemsnumerical examplesnumerical experimentspreconditioningparallel implementationGMRES methodminimal residual methoddense matrixHessenberg processKrylov method

Mathematics Subject Classification ID

Iterative numerical methods for linear systems (65F10) Parallel numerical computation (65Y05) Preconditioners for iterative methods (65F08)

Related Items

Heavy ball restarted CMRH methods for linear systems, Augmented and deflated CMRH method for solving nonsymmetric linear systems, The block Hessenberg process for matrix equations, Extended and rational Hessenberg methods for the evaluation of matrix functions, A flexible CMRH algorithm for nonsymmetric linear systems, Algorithms for the CMRH method for dense linear systems, Efficient variants of the CMRH method for solving a sequence of multi-shifted non-Hermitian linear systems simultaneously

Uses Software

• CMRH
• SparseMatrix

Cites Work

• A new look at CMRH and its relation to GMRES
• CMRH method as iterative solver for boundary element acoustic systems
• CMRH: A new method for solving nonsymmetric linear systems based on the Hessenberg reduction algorithm
• A parallel GMRES version for general sparse matrices
• A new implementation of the CMRH method for solving dense linear systems
• Approximate inverse preconditioners for some large dense random electrostatic interaction matrices
• The university of Florida sparse matrix collection
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• A Newton basis GMRES implementation
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