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一类求解非线性代数方程组的并行多分裂AOR算法

白中治

白中治. 一类求解非线性代数方程组的并行多分裂AOR算法[J]. 应用数学和力学, 1995, 16(7): 633-639.
引用本文: 白中治. 一类求解非线性代数方程组的并行多分裂AOR算法[J]. 应用数学和力学, 1995, 16(7): 633-639.
Bai Zhongzhi. Parallel Multisplitting AOR Method for Solving a Class of System of Nonlinear Algebraic Equations[J]. Applied Mathematics and Mechanics, 1995, 16(7): 633-639.
Citation: Bai Zhongzhi. Parallel Multisplitting AOR Method for Solving a Class of System of Nonlinear Algebraic Equations[J]. Applied Mathematics and Mechanics, 1995, 16(7): 633-639.

一类求解非线性代数方程组的并行多分裂AOR算法

Parallel Multisplitting AOR Method for Solving a Class of System of Nonlinear Algebraic Equations

  • 摘要: 本文提出了求解大型非线性代数方程组Aф(x)+Bψ(x)=b的并行多分裂AOR(Accelerated Overrela Xation)算法。在一定的条件下,证明了非线性代数方程组解的存在唯一性,并建立了新算法的全局收敛性理论。
  • [1] D.P.O Leary and R.E.White,Multisplittings of matrices and parallel solution of linear systems,SIAM J.Alg.Disc Meth.,6(1985),630-640.
    [2] R.E.White,A nonlinear parallel algorithm with application to the Stefan problem,SIAM J.Numer.Anal..23(1986),639-652.
    [3] Bai Zhongzhi,Parallel nonlinear AOR method and its convergence(1994).
    [4] R.E.White,Paralled algorithms for nonlinear problems,SIAM J.A份.Disc.Merh.,7(1986).137-149.
    [5] R.E.White,An enthalpy formulation of the Stefan problem,SIAM J.Nunrer.Anal.,19(1982).1129-1157.
    [6] R.E.White,The binary alloy solidfication problem:existence,uniqueness and numerical approximation,SIAM J.Nurner.Anal.,22(1985),205-244.
    [7] J.M.Ortega and W.C.Rheinboldt,Iterative Solutions of Nonlinear Equation irr Sereral Variables.Academic Press,New York(1970).
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出版历程
  • 收稿日期:  1994-05-27
  • 刊出日期:  1995-07-15

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