The survey of preconditioners used for accelerating the rate of convergence in the Gauss-Seidel method.

DOI10.1016/j.cam.2003.11.012zbMath1057.65022OpenAlexW2006807476MaRDI QIDQ1426801

Munenori Morimoto, Michio Sakakihara, Hiroshi Niki, Kyouji Harada

Publication date: 15 March 2004

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2003.11.012

zbMATH Keywords

preconditioningLaplace equationnonnegative matricesfinite differenceGauss-Seidel method

Mathematics Subject Classification ID

Iterative numerical methods for linear systems (65F10) Numerical computation of matrix norms, conditioning, scaling (65F35)

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Cites Work

• Unnamed Item
• Convergence of parallel multisplitting iterative methods for M-matrices
• Modified iterative methods for consistent linear systems
• Improving Jacobi and Gauss-Seidel iterations
• \(H\)-splittings and two-stage iterative methods
• Improving the modified Gauss-Seidel method for \(Z\)-matrices
• A comparison theorem for the iterative method with the preconditioner \((I+S_{max})\)
• Accelerated iterative method for \(Z\)-matrices
• Iterative Solution Methods
• On performance of SOR method for solving nonsymmetric linear systems