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記錄編號3387
狀態NC088FJU00479008
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學校名稱輔仁大學
系所名稱數學系
舊系所名稱
學號487366025
研究生(中)林素華
研究生(英)Lin, Su-hua
論文名稱(中)有理函數之■分段逼近
論文名稱(英)Segmented ■ Approximation by Rational Functions
其他題名
指導教授(中)楊南屏
指導教授(英)nanping Yang
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國圖全文開放日期.2005.01.01
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學位類別碩士
畢業學年度88
出版年
語文別英文
關鍵字(中)有理函數 分段逼近
關鍵字(英)Rational Functions Segmented Approximation
摘要(中)令 p 和 q 為次數最多一次的多項式。給一個在 ■[0, 1] 的連續可微函數,我們利用 p(t)/q(t) 這群有理函數對其做分段逼近。在適當的假設下, 我們發現在 ■[0, 1] 集合中會有一開子集,且在這集合內的每一元素都有唯一的 ■ 分段最佳有理逼近。
摘要(英)Let p and q be polynomials of degree at most 1. For a given continuous differentiable function from ■[0, 1], we consider segmented approximation from the family of functions p(t)/q(t) using ■ norm. Under appropriate hypothesis, we show that there is an opensubset of ■[0, 1] such that each element in it has an unique best segmented ■ rational approximation.
論文目次Contents 1 Preliminaries and Notions .................................................. 1 2 Existence and Characterization ........................................... 3 3 The Unity and Unique in Toplogical Sence........................... 6 3.1 The Unicity.......................................................................... 6 3.2 Uniquencess in Topological Sence.................................... 7 4 Concliuding Remarks........................................................ 23 References ............................................................................ 24
參考文獻References 1 D.J. Barrow, C.K. Chui, P.W. Smith and J.D. Ward, Unicity of best mean approximation by second order splines with variable knots, Math Comp. , 32(1978), 1131-1143. 2 E.W. Cheney , An Introduction to Approximation Theory, 2nd ed. Chelsea Publishing Company, 1981. 3 Chow, On the uniqueness of best ■[0,1] approximation by piecewise polymials with variable breakpoints, Math Comp. , 39(1982), 571-589 . 4 Y. Li, On the nonlinear rational approximation, 1998. 5 I. Singer, Best Approximation in Normed Linear Space by Elements and Linear Subspaces, Springer-Verlag, New York, 1970. 6 N. Yang, On the uinqueness of nonlinear approximation,Fu Jen Studies , 29(1995), 81-95.
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異動記錄M admin Y2008.M7.D3 23:17 61.59.161.35