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Original Articles

Adaptive gauss-seidel method for linear systems

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Pages 119-125 | Received 19 Apr 1993, Published online: 19 Mar 2007

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Ting-Zhu Huang & D. J. Evans. (2007) New estimations of the spectral radii of J, G–S and SOR iterative matrices for a class of linear systems. International Journal of Computer Mathematics 84:1, pages 23-31.
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Ahmet Yasar Özban. (2002) On Accelerated Iterative Methods for the Solution of Systems of Linear Equations. International Journal of Computer Mathematics 79:6, pages 765-773.
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M. Madalena Martins, D.J. Evans & W. Yousif. (2001) Further results on the preconditioned sor method. International Journal of Computer Mathematics 77:4, pages 603-610.
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Hisashi Kotakemori, Hiroshi Niki & Naotaka Okamoto. (1997) A generalization of the adaptive gauss-seidel method for Z-matrices. International Journal of Computer Mathematics 64:3-4, pages 317-326.
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Masataka Usui, Toshiyuki kohno & Hiroshi Niki. (1995) On the preconditioned sor method. International Journal of Computer Mathematics 59:1-2, pages 123-130.
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Toshiyuki Kohno, Hiroshi Niki & Masataka Usui. (1995) Multi-step preconditioned iteration method for nonsymmetric linear systems. International Journal of Computer Mathematics 56:3-4, pages 177-184.
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H. Saberi Najafi & S. A. Edalatpanah. (2014) A new family of (I+S)-type preconditioner with some applications. Computational and Applied Mathematics 34:3, pages 917-931.
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Seyoung Oh, Jae Heon Yun & Kyoum Sun Kim. (2015) ESOR METHOD WITH DIAGONAL PRECONDITIONERS FOR SPD LINEAR SYSTEMS. Journal of applied mathematics & informatics 33:1_2, pages 111-118.
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S. A. Edalatpanah & M. M. Rashidi. (2014) On the Application of Homotopy Perturbation Method for Solving Systems of Linear Equations. International Scholarly Research Notices 2014, pages 1-5.
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Yuzhuo Wang, Xiaohua Zhang, Yan Feng, Ruiting Shao, Xingchuang Xiong, Xiang Fang, Yulin Deng & Wei Xu. (2014) Characterization of geometry deviation effects on ion trap mass analysis: A comparison study. International Journal of Mass Spectrometry 370, pages 125-131.
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Jae Heon Yun, Hyo Jin Lim & Kyoum Sun Kim. (2014) PERFORMANCE COMPARISON OF PRECONDITIONED ITERATIVE METHODS WITH DIRECT PRECONDITIONERS. Journal of applied mathematics & informatics 32:3_4, pages 389-403.
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J.Y. Yuan & D.D. Zontini. (2012) Comparison theorems of preconditioned Gauss–Seidel methods for M-matrices. Applied Mathematics and Computation 219:4, pages 1947-1957.
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M. T. Darvishi, P. Hessari & Byeong-Chun Shin. (2011) Preconditioned modified AOR method for systems of linear equations. International Journal for Numerical Methods in Biomedical Engineering 27:5, pages 758-769.
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Hiroshi Niki, Toshiyuki Kohno & Munenori Morimoto. (2008) The preconditioned Gauss–Seidel method faster than the SOR method. Journal of Computational and Applied Mathematics 219:1, pages 59-71.
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Ji-cheng Li & Wei Li. (2008) The optimal preconditioner of strictly diagonally dominant Z-matrix. Acta Mathematicae Applicatae Sinica, English Series 24:2, pages 305-312.
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Zhuan-De Wang & Ting-Zhu Huang. (2006) The upper Jacobi and upper Gauss–Seidel type iterative methods for preconditioned linear systems. Applied Mathematics Letters 19:10, pages 1029-1036.
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Yong Zhang, Ting-Zhu Huang & Xing-Ping Liu. (2005) Modified iterative methods for nonnegative matrices and M-matrices linear systems. Computers & Mathematics with Applications 50:10-12, pages 1587-1602.
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Hiroyuki Hirano, Hideto Yoshida, Hiroyuki Ozoe & Naotaka Okamoto. (2004) A study on preconditioning iterative methods and relativity of pressure in the numerical calculation of fluid flow. Numerical Methods for Partial Differential Equations 20:5, pages 789-802.
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Hiroyuki Hirano, Hiroshi Niki, Toshiyuki Kohno & Naotaka Okamoto. (2001) Methods of Numerically Analyzing and Visually Measuring Transport Phenomena in Chemical Equipment. Acceleration of Numerical Calculation of Fluid Flow and Heat Transfer by Preconditioning Iterative Method.化学装置内の移動現象に関する数値解析と可視化計測法  前処理付反復法による熱流動問題の数値計算の高速化. KAGAKU KOGAKU RONBUNSHU 27:5, pages 547-553.
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Toshiyuki Kohno, Hisashi Kotakemori, Hiroshi Niki & Masataka Usui. (1997) Improving the modified Gauss-Seidel method for Z-matrices. Linear Algebra and its Applications 267, pages 113-123.
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Hisashi Kotakemori, Hiroshi Niki & Naotaka Okamoto. (1997) Convergence of a preconditioned iterative method for H-matrices. Journal of Computational and Applied Mathematics 83:1, pages 115-118.
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Hisashi Kotakemori, Hiroshi Niki & Naotaka Okamoto. (1996) Accelerated iterative method for Z-matrices. Journal of Computational and Applied Mathematics 75:1, pages 87-97.
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