| 求解非线性算子方程的加速迭代格式 |
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| 引用本文： | 侯素青,李鹤,吴开谡.求解非线性算子方程的加速迭代格式[J].应用泛函分析学报,2012(2):177-182. |
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| 作者姓名： | 侯素青 李鹤 吴开谡 |
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| 作者单位： | 北京化工大学数学与信息科学系 |
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| 基金项目： | 北京化工大学青年科学基金(QN0622) |
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| 摘 要： | 研究非线性算子方程的近似求解方法.首先对通常的求解非线性方程加速迭代格式进行推广,得到高阶收敛速度的加速迭代格式,最后把这种加速迭代格式推广到非线性算子方程的求解中去,利用非线性算子的渐进展开,证明了这种加速格式具有三阶的收敛速度.
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| 关 键 词： | 加速格式 收敛阶 非线性算子方程 导算子 |
Accelerative Iterative Formula for the Non-linear Operator Equation |
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| HOU Suqing,LI He,WU Kaisu.Accelerative Iterative Formula for the Non-linear Operator Equation[J].Acta Analysis Functionalis Applicata,2012(2):177-182. |
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| Authors: | HOU Suqing LI He WU Kaisu |
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| Institution: | Department of Mathematics and Information Science,Beijing University of Chemical Technology,Beijing 100029, China |
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| Abstract: | Approximate solving method for the non-linear operator equation is investigated in this paper.First,we generalize the accelerative iterative formula of the non-linear functional equation so that we obtain the high-speed convergent iterative formula.Finally,the new accelerative iterative formula has been generalized for the non-linear operator equation.Using the asymptotic expansions of the non-linear operator,we prove that the new accelerative iterative formula is convergence with order 3. |
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| Keywords: | accelerative schemes order of convergence non-linear operator equation derivative operator |
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