| 一类求解非线性奇异方程组的牛顿改进算法 |
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| 引用本文： | 吕巍,魏良亭,冯恩民. 一类求解非线性奇异方程组的牛顿改进算法[J]. 控制与决策, 2017, 32(12): 2240-2246 |
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| 作者姓名： | 吕巍 魏良亭 冯恩民 |
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| 作者单位： | 上海大学数学系,上海200444,大连理工大学数学科学学院,辽宁大连116024,大连理工大学数学科学学院,辽宁大连116024 |
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| 基金项目： | 国家自然科学青年基金项目(11101262)；上海市重点学科项目(S30104)；上海高校一流学科项目(B类). |
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| 摘 要： | 受一个求解非线性奇异方程组迭代格式的启示,将两种牛顿改进算法推广成一般形式,并将其发展为一类求解具有奇异雅可比矩阵的非线性方程组的牛顿改进算法.首先,描述这类新算法的迭代格式,并导出其收敛阶,该新格式每步迭代仅需计算一次函数值和一次导函数值;然后,对测试函数进行检验,并与牛顿算法及其他奇异牛顿算法进行比较,从而验证该算法的快速收敛性;最后,通过两个实际问题验证所提出算法的有效性.
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| 关 键 词： | 牛顿算法 奇异雅可比矩阵 非线性方程组 收敛阶 |
A modification of Newton's method solving non-linear equations with singular Jacobian |
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| LV Wei,WEI Liang-ting and FENG En-min. A modification of Newton's method solving non-linear equations with singular Jacobian[J]. Control and Decision, 2017, 32(12): 2240-2246 |
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| Authors: | LV Wei WEI Liang-ting FENG En-min |
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| Affiliation: | Department of Mathematics,Shanghai University,Shanghai 200444,China,Department of Mathematics,Shanghai University,Shanghai 200444,China and School of Mathematical Sciences,Dalian University of Technology,Dalian 116024,China |
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| Abstract: | Motivated by a singular technique for root-finding, two Newton''s methods are generalized to a class of iteration formats, on the basis of which, a modification of the Newton''s method solving non-linear equations with singular Jacobian is presented.Firstly, the new rule is described and its convergence order is analyzed. The modified singular method requires one function and one first derivative evaluations per step.Then, numerical examples demonstrate the faster convergence achieved with this modification than Newton''s method and some singular schemes.Finally, two practical problems are given to illustrate the effectiveness of the proposed method. |
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