理论数学  >> Vol. 3 No. 6 (November 2013)

三次样条插值函数的新解法
New Solution of Cubic Spline Interpolation Function

DOI: 10.12677/PM.2013.36055, PDF, HTML, 下载: 3,028  浏览: 7,938 

作者: 刘永春, 王 强:安徽理工大学理学院,淮南

关键词: 三次样条插值第二边界条件二阶导数Cubic Spline Interpolation; Second Boundary; Second Derivative

摘要: 本文在分析了三次样条插值里三转角算法的基础上,对第二种边界条件的情形进行了推广,研究了此情形下任意两插值点二阶导数已知的样条函数的解法。文章的最后,通过一个例子,说明了此计算方法。
>In this article, based on analysis of three turning angles algorithm of cubic spline interpolation, the cubic spline interpolation is generalized on the condition of the second boundary. The methods are presented on the condition that the second derivative of arbitrary two nodes is given. At the end of the article, this cal- culation method is illustrated through an example.

文章引用: 刘永春, 王强. 三次样条插值函数的新解法[J]. 理论数学, 2013, 3(6): 362-367. http://dx.doi.org/10.12677/PM.2013.36055

参考文献

[1] 朱立勋, 安玉萍 (2007) 一个关于三次样条插值收敛性的证明. 吉林建筑工程学院学报, 3, 94-96.
[2] 郭昌言, 高尚 (2011) 三次样条插值的推广. 科学技术与工程, 7, 1507-1510.
[3] 许小勇, 钟太勇 (2006) 三次样条插值函数的构造与Matlab实现. 兵工自动化, 11, 76-78.
[4] Clements, J.C. (1990) Convexity-preserving pieeewise rational cH-bic interDolation. SIAM Journal on Numerical Analysis, 27, 38-46.
[5] Duan, Q., Zhang, Y.F. and Twizell, E.H. (2006) A bivariate rational interpolation and the properties. Applied Mathematics and Computation, 179, 190-199.
[6] 林成森 (1997) 数值计算方法.科学出版社, 北京, 152-164.
[7] 张诚坚 (1999) 计算方法.高等教育出版社, 北京, 77-81.
[8] 王能超 (2010) 计算方法——算法设计及其MATLAB实现. 华中科技大学出版社, 武汉, 45-50.
[9] Delbourgo, R. (1993) Accurate C2 rational interpolations intension. SIAM Journal on Numerical Analysis, 30, 595-603.