MQ拟插值算子的构造及其相关性质

发布时间：2018-03-22 00:29

本文选题：MQ拟插值　切入点：径向基函数插值　出处：《东北师范大学》2015年硕士论文　论文类型：学位论文

【摘要】：本文通过对径向基函数插值、Multi-Quadric拟插值的研究,对已有的拟插值算子LAf(x)、LBf(x)、LCf(x)和LDf(x)进行了分析,文中验证了它们的线性再生性、保单调性和保凸性,并给出了LAf(x)、LBf(x)、LCf(x)和LDf(x)逼近一些函数的图像。本文的主要工作是构造了四种全新的拟插值算子L1f(x)、L2f(x)、L3f(x)和L4f(x),其中L1f(x)、L2f(x)是在LDf(x)和Lcf(x)的基础上进行的改进,对于L1f(x)、L2f(x)中出现的端点处导数值,文中利用差商来代替,从而得到算子L3f(x)和L4f(x),这解决了端点处导数值难得到的问题,也更适合实际应用。文章同时还讨论了它们的保单调性和保凸性。最后我们用新构造的拟插值算子根据已知的数据分别画出了逼近一维、二维、三维函数的图像,体现了其逼近程度,数值算例给出了原有拟插值算子与新构造的拟插值算子之间的插值结果比较,相对原有的拟插值算子,新构造的拟插值算子的误差更小,结果更好。
[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.
【学位授予单位】：东北师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O241.3

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