非线性算子方程的加速迭代公式

应用泛函分析学报 Pub Date : 2012-01-01 DOI:10.3724/SP.J.1160.2012.00177

Suqing Hou, He Li, Kaisu Wu

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引用次数: 0

摘要

本文研究了非线性算子方程的近似求解方法。首先，对非线性泛函方程的加速迭代公式进行了推广，得到了高速收敛的迭代公式。最后，对非线性算子方程推广了新的加速迭代公式。利用非线性算子的渐近展开式，证明了新的加速迭代公式是3阶收敛的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Accelerative Iterative Formula for the Non-linear Operator Equation

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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应用泛函分析学报

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