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博碩士論文 etd-0629110-163913 詳細資訊
Title page for etd-0629110-163913
論文名稱
Title
平均算子及其應用
Averaged mappings and it's applications
系所名稱
Department
畢業學年期
Year, semester
語文別
Language
學位類別
Degree
頁數
Number of pages
24
研究生
Author
指導教授
Advisor
召集委員
Convenor
口試委員
Advisory Committee
口試日期
Date of Exam
2010-06-17
繳交日期
Date of Submission
2010-06-29
關鍵字
Keywords
分裂可行性問題、弱收斂、非擴張映射、平均算子、多重分裂可行性問題、Krasnosel'skii-Mann 演算法
split feasibility problem, weak convergence, multiple-set split feasibility problem, Krasnosel'skii-Mann algorithm, averaged mapping, nonexpansive mapping
統計
Statistics
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中文摘要
Krasnosel’skii-Mann 演算法是一個數列{x_n }經由以下的迭代方式 x_{n+1} =(1- α\_n)x_n+ α\_nT_nx_n
所生成,其中{α\_n }為(0,1)區間中的數列且{T_n}為非擴張映射。我們將介紹KM 演算法並且証明由KM 演算法生成的{x_n }會弱收斂至T 的固定點,而再利用這個結果來解決分裂可行性問題。這篇論文主要目的是應用KM 演算法去解分裂可行性問題、多重分裂可行性問題和其他的一些應用。
Abstract
A sequence fxng generates by the formula
x_{n+1} =(1- α\_n)x_n+ α\_nT_nx_n is called the Krasnosel'skii-Mann algorithm, where {α\_n} is a sequence in (0,1) and {T_n} is a sequence of nonexpansive mappings. We introduce KM algorithm and prove that the sequence fxng generated by KM algorithm converges weakly. This result is used to solve the split feasibility problem which is to find a point x with the property that x ∈ C and Ax ∈ Q, where C and Q are closed convex subsets form H1 to H2, respectively, and A is a bounded linear operator form H1 to H2. The purpose of this paper is to present some results which apply KM algorithm to solve the split feasibility problem, the multiple-set split feasibility problem and other applications.
目次 Table of Contents
1 Introduction 1
2 Preliminaries 4
3 Convergence of an averaged mapping 6
4 Application 14
References 18
參考文獻 References
[1] F. Alvarez 2004 Weak convergence of a relaxed and inertial hybird porjectionproximal point algorithm for maximal monotone operators in Hilbert space
SIAM J.Optim. 14 773-82
[2] C.L. Byrne 2004 A unified treatment of some iterative algorithms in signal
processing and image reconstruction Inverse Problems 20 103-20
[3] Y. Censor, T. Elfving, N. Kopf and T. Bortfeld 2005 THe multiple-sets splits
feasibility problem and its applications for inverse problem Inverse Problems
21 2071-84
[4] K. Geobel, W.A. Kirk, Topics in metric fixed point theory, Cambridge University Press, 1990. Cambridge stud. Adv. Math., Vol. 28
[5] S Reich 1979 Weak convergence theorems for nonexpansive mappings in Banach spaces J. Math. Anal. Appl. 67 274-6
[6] Q. Yang and J. Zhao 2004 The relaxed CQ algorithm for solving the split
feasibility problem Inverse Problems 20 1261-6
[7] Q. Yang and J. Zhao 2005 Several solution methods for the split feasibility
problem Inverse Problems 21 1791-9
[8] Q. Yang and J. Zhao 2006 Generalized KM theorems and their applications
Inverse Problems 22 833-44
[9] H.K. Xu 1991 Inequalities in Banach spaces with applications Nonlinear Anal.
16 1127-38
[10] H.K. Xu 2006 A variable Krasnoselskii-Mann algorithm and the multiple-set
split feasibility problem Inverse Problems 22 2021-34
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