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山东大学学报（理学版） ›› 2018, Vol. 53 ›› Issue (2): 18-24.doi: 10.6040/j.issn.1671-9352.0.2017.292

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椭圆方程柯西问题磨光正则化参数的后验选取

丁凤霞,程浩*   

  1. 江南大学理学院, 江苏 无锡 214122
  • 收稿日期:2017-06-14 出版日期:2018-02-20 发布日期:2018-01-31
  • 通讯作者: 程浩(1983— ),男,副教授,研究方向为数学物理方程反问题.E-mail:chenghao@jiangnan.edu.cn E-mail:2282223175@qq.com
  • 作者简介:丁凤霞(1992— ),女,硕士研究生,研究方向为数学物理方程反问题.E-mail:2282223175@qq.com
  • 基金资助:
    国家自然科学基金资助项目(11426117);江苏省自然科学基金资助项目(BK20130118);中国石油化工股份有限公司科技资助项目(P15165)

A posteriori choice rule for the mollification regularization parameter for the Cauchy problem of an elliptic equation

DING Feng-xia, CHENG Hao*   

  1. School of Science, Jiangnan University, Wuxi 214122, Jiangsu, China
  • Received:2017-06-14 Online:2018-02-20 Published:2018-01-31

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摘要： 通过将带有参数的Gaussian函数和测量数据作卷积,把不适定问题转化为适定问题进行求解,给出基于Morozov偏差原理的后验参数选取规则并得到了精确解和正则近似解之间的误差估计。数值实验表明了磨光正则化后验参数选取规则的有效性。

关键词: 椭圆方程柯西问题, 磨光正则化方法, 数值实验, 后验参数选取, 误差估计

Abstract: We transform the ill-posed problem into a well-posed problem by convolutioning the Gaussian function with parameters and the measurement data. A posteriori parameter choice rule is given which is based on Morozovs discrepancy principle and the error estimates between the exact solution and its approximation are also given. Numerical experiments show the validity of mollification regularization posteriori parameter choice rule.

Key words: mollification regularization method, posteriori parameter choice, error estimation, the Cauchy problem of an elliptic equation, numerical experiment

中图分类号: 

  • O241.8
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