The Landweber Iterative Regularization Method for Solving the Cauchy Problem of the Modified Helmholtz Equation

被引：2
|
作者：
Chen, Yong-Gang [1 ]
Yang, Fan [2 ]
Ding, Qian [2 ]
机构：
[1] China Univ Petr, Sch Sci, Qingdao 266580, Peoples R China
[2] Lanzhou Univ Technol, Sch Sci, Lanzhou 730050, Peoples R China
来源：
SYMMETRY-BASEL | 2022年 / 14卷 / 06期
基金：
中国国家自然科学基金;
关键词：
modified Helmholtz equation; ill-posed problem; error estimation; Landweber iterative method;
D O I：
10.3390/sym14061209
中图分类号：
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
In this manuscript, the Cauchy problem of the modified Helmholtz equation is researched. This inverse problem is a serious ill-posed problem. The classical Landweber iterative regularization method is designed to find the regularized solution of this inverse problem. The error estimations between the exact solution and the regularization solution are all obtained under the a priori and the a posteriori regularization parameter selection rule. The Landweber iterative regularization method can also be applied to solve the Cauchy problem of the modified Helmholtz equation on the spherically symmetric and cylindrically symmetric regions.
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页数：22
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