解非线性方程组的一类算法 |
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引用本文: | 陈志,邓乃扬,薛毅.解非线性方程组的一类算法[J].计算数学,1992,14(3):322-329. |
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作者姓名: | 陈志 邓乃扬 薛毅 |
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作者单位: | 北京工业大学应用数学系
(陈志,邓乃扬),北京工业大学应用数学系(薛毅) |
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摘 要: | §1.引言 求解线性方程组 a_i~Tx=b_i,i=1,2,…,n,(1.1)其中a_1,a_2,…,a_n线性无关. 设y~((1))为初值,U~((1))为任意非奇异n阶矩阵,我们用如下方法求解方程组(1.1). 先考虑前k-1个方程组成的亚定方程组 a_i~Tx=b_i,i=1,2,…,k-1.设{U~((k))}={a_1,a_2,…,a_(k-1)},这里{U~((k))}表示由U~((k))的列组成的子空间.显然,rank(U~((k)))=n-b+1.若y~((k))是相应的亚定方程的一个特解,则将其看作方程组
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关 键 词: | 非线性方程组 解 算法 |
A Class of Methods for Solving Nonlinear Systems of Equations |
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Institution: | Chen Zhi;Deng Nai-yang;Xue Yi Beijing Polytechnic University |
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Abstract: | A class of algorithms for solving nonlinear systems of equations is proposed.Compared with the discrete Newton method, this class has the same quadratic co-nvergency, but its number of evaluations of the function is less than that of thediscrete Newton method per cycle. Some efficient algorithms can be obtained whenthe parameter is chosen by a different means. The nonlinear ABS algorithm, andthe Brown and Brent method are special cases of this class. The numerical exam-ples have showed its effectiveness. |
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