A regularization framework for mildly ill-posed problems connected with pseudo-differential operator

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:341

Article

Xiong, Xiangtuan¹  Zhuang, E.¹  Xue, Xuemin¹  Qian, Zhi² 

[1] Northwest Normal Univ, Dept Math, Lanzhou, Gansu, Peoples R China

[2] Nanjing Univ, Dept Math, Nanjing, Jiangsu, Peoples R China

关键词: III-posed problems;    Fractional Tikhonov regularization;    Error estimate;    Pseudo-differential operator;   

DOI  :  10.1016/j.cam.2018.03.009

来源: Elsevier

【 摘 要 】

Recently filter-based regularization methods have been well investigated for ill-posed problems when the forward operators are compact. There are many ill-posed problems connected with pseudo-differential operators. But there is no uniform method for this kind of problems. The work on generalization of filter-based regularization methods to pseudo differential operator is necessary. In this paper, we present a regularization framework for solving the mildly ill-posed problems involved pseudo-differential operators. A general regularization method for this kind of problems is given. The order-optimal error estimates are derived under the usual source conditions. As an example, a new fractional Tikhonov regularization method could be cast into the general framework. Numerical experiments are conducted for showing the validity of the new fractional Tikhonov method. (C) 2018 Elsevier B.V. All rights reserved.

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