論文使用權限 Thesis access permission:校內校外均不公開 not available
開放時間 Available:
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論文名稱 Title |
平均算子及其應用 Averaged mappings and it's applications |
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系所名稱 Department |
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畢業學年期 Year, semester |
語文別 Language |
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學位類別 Degree |
頁數 Number of pages |
24 |
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研究生 Author |
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指導教授 Advisor |
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召集委員 Convenor |
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口試委員 Advisory Committee |
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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 |
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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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