| 非线性方程组的Newton流线法 |
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| 引用本文： | 陈传淼,胡宏伶,雷蕾,曾星星.非线性方程组的Newton流线法[J].计算数学,2012,34(3):235-258. |
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| 作者姓名： | 陈传淼 胡宏伶 雷蕾 曾星星 |
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| 作者单位： | 高性能计算与随机信息处理省部共建教育部重点实验室 湖南师范大学数学与计算机科学学院, 长沙 410081 |
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| 摘 要： | 为求解非线性方程组F(x)=0, 研究了Newton流方程xt=V(x)=-(DF(x))-1F(x),x(0)=x0,及数值Newton流xj+1=xj+hV(xj),h∈(0,1].导出了减幅指标gj(h)=||F(xj+1)||/||F(xj)||=1-h+h2djh<1和m重根x*附近的表示gj(h)=(1-h/m)m+h2O(||xj-x*||).最后基于4个可计算量gj,dj,Kj,qj,提出了新的Newton流线法,如果投入大量的随机初始点, 能找到所有实根、重根和复根.
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| 关 键 词： | 非线性方程组 Newton流线法 中心场 可计算量 求所有的根 |
| 收稿时间： | 2011-06-26; |
NEWTON FLOW METHOD FOR NONLINEAR SYSTEMS OF EQUATIONS |
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| Chen Chuanmiao
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Hu Hongling
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Lei Lei
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Zeng Xingxing.NEWTON FLOW METHOD FOR NONLINEAR SYSTEMS OF EQUATIONS[J].Mathematica Numerica Sinica,2012,34(3):235-258. |
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| Authors: | Chen Chuanmiao Hu Hongling Lei Lei Zeng Xingxing |
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| Institution: | Key Laboratory of High Performance Computing and Stochastic Information Processing (Ministry of Education of China), College of Mathematics and Computer Science, Hunan Normal University, Changsha 410081, China |
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| Abstract: | To solve nonlinear systems of equations F（x）=0,Newton’s flow equation xt（t）= V（x）=-（DF（x））-1F（x）,x（0）=x0 and its numerical flow xj+1=xj+hV（xj） for h G(0,1] are studied.The damped index gj（h）=||F(xj+1)||/||F（xj）||=1-h + h2d3（h）|<1 and refine expression gj（h）—（1-h/m）m + h2O（||xj—x*||） near the m-ple root x* are derived. Finally based on fourth computable quantities gj,dj,Kj,qj,a new Newton flow algorithm is proposed,which can find all real,multiple and complex roots,if put into a large number of stochastic initial points. |
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| Keywords: | nonlinear system of equations Newton flow-line method central field two basic equalities A posteriori estimator find all roots |
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