Convergence analysis of M-iteration for 𝒢-nonexpansive mappings with directed graphs applicable in image deblurring and signal recovering problems

IF 2 3区数学 Q1 MATHEMATICS

Demonstratio Mathematica Pub Date : 2023-01-01 DOI:10.1515/dema-2022-0234

Chonjaroen Chairatsiripong, D. Yambangwai, T. Thianwan

引用次数: 0

Abstract

Abstract In this article, weak and strong convergence theorems of the M-iteration method for 𝒢-nonexpansive mapping in a uniformly convex Banach space with a directed graph were established. Moreover, weak convergence theorem without making use of Opial’s condition is proved. The rate of convergence between the M-iteration and some other iteration processes in the literature was also compared. Specifically, our main result shows that the M-iteration converges faster than the Noor and SP iterations. Finally, the numerical examples to compare convergence behavior of the M-iteration with the three-step Noor iteration and the SP-iteration were given. As application, some numerical experiments in real-world problems were provided, focused on image deblurring and signal recovering problems.

查看原文本刊更多论文

𝒢-nonexpansive有向图映射的m -迭代收敛性分析，适用于图像去模糊和信号恢复问题

摘要本文建立了具有有向图的一致凸Banach空间𝒢-nonexpansive映射的m迭代法的弱收敛定理和强收敛定理。此外，还证明了不使用Opial条件的弱收敛定理。比较了m迭代法与文献中其他迭代法的收敛速度。具体而言，我们的主要结果表明m迭代比Noor和SP迭代收敛得更快。最后，通过数值算例比较了m迭代与三步Noor迭代和sp迭代的收敛性。作为应用，提供了一些实际问题的数值实验，重点研究了图像去模糊和信号恢复问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Demonstratio Mathematica MATHEMATICS-

CiteScore

2.40

自引率

5.00%

发文量

审稿时长

35 weeks

期刊介绍： Demonstratio Mathematica publishes original and significant research on topics related to functional analysis and approximation theory. Please note that submissions related to other areas of mathematical research will no longer be accepted by the journal. The potential topics include (but are not limited to): -Approximation theory and iteration methods- Fixed point theory and methods of computing fixed points- Functional, ordinary and partial differential equations- Nonsmooth analysis, variational analysis and convex analysis- Optimization theory, variational inequalities and complementarity problems- For more detailed list of the potential topics please refer to Instruction for Authors. The journal considers submissions of different types of articles. "Research Articles" are focused on fundamental theoretical aspects, as well as on significant applications in science, engineering etc. “Rapid Communications” are intended to present information of exceptional novelty and exciting results of significant interest to the readers. “Review articles” and “Commentaries”, which present the existing literature on the specific topic from new perspectives, are welcome as well.