| 松弛型并行多分裂方法解非线性方程组的安全界 |
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| 引用本文： | 谷同祥,王能超.松弛型并行多分裂方法解非线性方程组的安全界[J].应用数学,1995(3). |
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| 作者姓名： | 谷同祥 王能超 |
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| 作者单位： | 河南师范大学数学系，华中理工大学并行计算研究所 新乡 453002，武汉 430074 |
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| 基金项目： | The National Funds of Natural Science |
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| 摘 要： | 本文对某些非线性方程组F(x)=0,导出了一个算法,用它可以迭代建立F(x)=0的解的紧致上、下界。算法基于某些矩阵的多分裂,因此具有自然的并行性。我们证明了趋向于解的界之收敛原则,给出了参数的收敛性区域并考察了方法的收敛速度。
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| 关 键 词： | 非线性方程组 迭代法 并行算法 多分裂方法 区间算法 |
Safe Bounds for the Solutions of Nonlinear Problems Using a Relaxed Parallel Multisplitting Method |
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| Gu Tongxiang.Safe Bounds for the Solutions of Nonlinear Problems Using a Relaxed Parallel Multisplitting Method[J].Mathematica Applicata,1995(3). |
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| Authors: | Gu Tongxiang |
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| Abstract: | For some systems of nonlinear equations F(x) = 0,we derive an algorithem which it-eratively constructs tight lower and upper bounds for the zeros of F. The algorithm is based on a multisplitting of certain matrices thus showing a natural parallelism. We prove criteria for the convergence of the bounds towards the zeros,give the regions of parameters for convergence and investigate the speed of convergence. |
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| Keywords: | Nonlinear system Iterative method Parallel algorithm Multisplitting method Interval algorithm |
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