On the generalisation of the basic iterative methods for the solution of linear systems

DOI10.1080/00207168308803395zbMath0517.65012OpenAlexW2167055243MaRDI QIDQ3666129

Apostolos Hadjidimos

Publication date: 1983

Published in: International Journal of Computer Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00207168308803395

zbMATH Keywords

splittingsuccessive overrelaxation methodGauss-Seidel methodJacobi methodextrapolated method

Mathematics Subject Classification ID

Iterative numerical methods for linear systems (65F10)

Related Items

Generalized Stein-Rosenberg theorems for the regular splittings and convergence of some generalized iterative methods, Generalized extrapolation principle and convergence of some generalized iterative methods, Stepsize restrictions for stability in the numerical solution of ordinary and partial differential equations, A survey of the iterative methods for the solution of linear systems by extrapolation, relaxation and other techniques, A survey of AOR and TOR methods, The upper bound of the spectral radius of M^-1N and convergence of some iterative methods, Convergence conditions for some generalized iterative methods, THE PARALLEL MULTISPLITTING GENERALIZED ITERATIVE METHODS, The closure property of the Schur complement for Nekrasove matrices and its applications in solving large linear systems with Schur-based method, Convergence theory for the general GAOR type iterative method and the MSOR iterative method applied to \(H\)-matrices, Further results on regular splittings and their applications to some iterative methods, A class of parallel decomposition-type relaxation methods for large sparse systems of linear equations, Convergence for a general form of the GAOR method and its application to the MSOR method, On the convergence of some generalized iterative methods

Cites Work

• Extensions of the Ostrowski-Reich theorem for SOR iterations
• The principle of extrapolation in connection with the accelerated overrelaxation method
• On recurring theorems on diagonal dominance
• M-matrix characterizations. I: nonsingular M-matrices
• Some basic results on M-matrices in connection with the accelerated overrelaxation (AOR) method
• Über reguläre Zerlegungen von Matrizen und einige Anwendungen
• On Different Splittings and the Associated Iteration Methods
• Frobenius Theory of Positive Operators: Comparison Theorems and Applications
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