Banach空间中迭代正则化方法的收敛性分析
PDF下载 (336)王佳敏,王金平.Banach空间中迭代正则化方法的收敛性分析[J].宁波大学学报(理工版),2019,32(1):84-88.DOI:
WANG Jia-min,WANG Jin-ping.Convergence analysis of iterative regularization methods in Banach spaces[J].Journal of Ningbo University(Natural Science & Engineering Edition),2019,32(1):84-88.DOI:
| Title: | Convergence analysis of iterative regularization methods in Banach spaces |
| 作者: | 王佳敏, 王金平 |
| Author(s): | WANG Jia-min, WANG Jin-ping |
| 关键词: | Landweber-Kaczmarz迭代算法; 收敛性; Bregman距离; Fréchet可微; Fréchet differentiable |
| Keywords: | Landweber-Kaczmarz iterative algorithm; convergence; Bregman distance |
| 分类号: | O177; O175.5 |
| 文献标识码: | A |
| 摘要: | 利用Landweber-Kaczmarz迭代算法研究非线性不适定问题. 首先, 在Banach空间引入Bregman距离, 构造合适的步长, 说明Bregman距离序列在迭代算法中是单调递减的. 然后, 由凸分析、对偶映射和Fréchet可微的性质得到迭代算法具有收敛性. |
| Abstract: | In this paper, we study the Landweber-Kaczmarz iterative algorithm for nonlinear ill-posed problems. We first introduce the iterative step, and then derive the sequence of Bregman distance which is monotonously decreasing in Banach space. With the convex analysis, duality mapping and Fréchet differentiable, we succeed in obtaining the convergence of the iterative algorithm. |
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| 备注/Memo: | 收稿日期: 2018－02－06. 宁波大学学报（理工版）网址: http://journallg.nbu.edu.cn/基金项目: 国家自然科学基金（61271398）; 宁波大学研究生科研创新基金（G17068）.第一作者: 王佳敏（1994－）, 女, 河南信阳人, 在读硕士研究生, 主要研究方向: 积分变换与图像处理. E-mail: 1432810637@qq.com*通信作者: 王金平（1962－）, 男, 湖北武汉人, 博士/教授, 主要研究方向: 积分变换与图像处理. E-mail: wangjinping@nbu.edu.cn 宁波大学学报（理工版）网址：http://journallg.nbu.edu.cn/ |
