本文選題：MQ擬插值　切入點：徑向基函數(shù)插值　出處：《東北師范大學》2015年碩士論文　論文類型：學位論文

【摘要】：本文通過對徑向基函數(shù)插值、Multi-Quadric擬插值的研究,對已有的擬插值算子LAf(x)、LBf(x)、LCf(x)和LDf(x)進行了分析,文中驗證了它們的線性再生性、保單調(diào)性和保凸性,并給出了LAf(x)、LBf(x)、LCf(x)和LDf(x)逼近一些函數(shù)的圖像。本文的主要工作是構(gòu)造了四種全新的擬插值算子L1f(x)、L2f(x)、L3f(x)和L4f(x),其中L1f(x)、L2f(x)是在LDf(x)和Lcf(x)的基礎上進行的改進,對于L1f(x)、L2f(x)中出現(xiàn)的端點處導數(shù)值,文中利用差商來代替,從而得到算子L3f(x)和L4f(x),這解決了端點處導數(shù)值難得到的問題,也更適合實際應用。文章同時還討論了它們的保單調(diào)性和保凸性。最后我們用新構(gòu)造的擬插值算子根據(jù)已知的數(shù)據(jù)分別畫出了逼近一維、二維、三維函數(shù)的圖像,體現(xiàn)了其逼近程度,數(shù)值算例給出了原有擬插值算子與新構(gòu)造的擬插值算子之間的插值結(jié)果比較,相對原有的擬插值算子,新構(gòu)造的擬插值算子的誤差更小,結(jié)果更好。
[Abstract]:In this paper, based on the study of the Radial basis function interpolation and Multi-Quadric quasi interpolation, the existing quasi interpolation operators LAfUX, LBFX, LCfNX) and LDfHX) are analyzed. The linear regeneration, monotonicity and convexity of these quasi interpolation operators are verified in this paper. In this paper, four new quasi-interpolation operators, L _ 1f _ n _ (x) and L _ (1f ~ (X)) and L _ 4f _ (X), are presented, which are improved on the basis of LDF ~ ((x)) and Lcfnx). The main work of this paper is to construct four new quasi-interpolation operators, L _ 1f _ n _ (x) and L _ (4) f _ (x), which are improved on the basis of L _ 1f ~ (~ +) and L _ (cfn) _ x), and the values of the terminal conductance at the end of L _ 1f _ XN _ XN _ (L2fN _ x) are constructed. In this paper, the difference quotient is used to replace the operator L _ 3fN _ x) and L _ 4f ~ (x), which solves the problem that it is difficult to obtain the derivative value at the end point. This paper also discusses their monotonicity and convexity. Finally, we draw approximate images of one-dimensional, two-dimensional and three-dimensional functions according to the known data by using the newly constructed quasi-interpolation operator. The numerical example shows the comparison between the original quasi-interpolation operator and the new quasi-interpolation operator. Compared with the original quasi-interpolation operator, the new quasi-interpolation operator has smaller error and better result.
【學位授予單位】：東北師范大學
【學位級別】：碩士
【學位授予年份】：2015
【分類號】：O241.3

【參考文獻】

相關(guān)博士學位論文 前2條

1 陳榮華;徑向基函數(shù)擬插值理論及其在微分方程數(shù)值解中的應用[D];復旦大學;2005年

2 高文武;擬插值的若干理論及其應用[D];復旦大學;2012年

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本文編號：1646264