| 非线性不适定问题一种双循环的牛顿型迭代格式 |
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| 引用本文： | 张瑰,黄思训.非线性不适定问题一种双循环的牛顿型迭代格式[J].数学年刊A辑(中文版),2003(3). |
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| 作者姓名： | 张瑰 黄思训 |
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| 作者单位： | 解放军理工大学理学院数理系，解放军理工大学气象学院军事气象系 南京 211101，南京 211101 |
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| 基金项目： | 国家自然科学基金(NO.40075014) |
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| 摘 要： | 本文研究非线性算子方程F(x)=y的解,结合最速下降法,Newton-Landweber迭代格式及正则化思想,在F满足适当的条件下,构造出新的双循环迭代格式。本文对格式的收敛性进行了严格论证,并估计出迭代格式的收敛精度。
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| 关 键 词： | 非线性算子方程 非线性不适定问题 牛顿型迭代格式 迭代终止原则 收敛阶估计 |
ON A NEWTON-TYPE METHOD FOR THE REGULARIZATION OF NONLINEAR ILL-POSED PROBLEMS |
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| ZHANG Gui HUANG Sixun
Institute of Science,PLA University of Science & Technology,Nanjing ,China.ON A NEWTON-TYPE METHOD FOR THE REGULARIZATION OF NONLINEAR ILL-POSED PROBLEMS[J].Chinese Annals of Mathematics,2003(3). |
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| Authors: | ZHANG Gui HUANG Sixun
Institute of Science PLA University of Science & Technology Nanjing China |
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| Institution: | ZHANG Gui HUANG Sixun
Institute of Science,PLA University of Science & Technology,Nanjing 211101,China.
Institute of Meteorology,PLA University of Science & Technology,Nanjing 211101,China. E-mail. huangsx@publicl.ptt.js.cn |
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| Abstract: | This paper considers a Newton-type method, for regularizing the abstract nonlinear ill-posed operator equation F(x) = y. Under certain smoothness conditions on the nonlinear operator, the authors obtain the local convergence of the method. By further assumptions on the closeness and smoothness of the exact solution, a stopping rule to terminate the iteration is proposed and the suitable rates of convergence is derived. |
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| Keywords: | Nonlinear operation equations Nonlinear ill-posed problems Newton-type method Stopping rule Convergence rate |
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