四次样条插值函数的研究  

Researches on the Four Times Spline Interpolation Functions

作　　者：郭芹[1] 魏华 孙红卫[1] 

机构地区：[1]济南大学理学院,山东济南250022 [2]牡丹江市第二中学,黑龙江牡丹江157000

出　　处：《牡丹江教育学院学报》2009年第6期62-65,共4页Journal of Mudanjiang College of Education

基　　金：山东省自然科学基金(编号Y2007A11);济南大学博士基金(编号XBS0832)

摘　　要：主要研究了四次样条插值函数的存在唯一性,通过给出三种边界条件,利用三弯矩法的思想,建立求解四次样条插值函数的线性方程组。在等步长的条件下,研究了线性方程组的系数矩阵,在三种边界条件下,证明了系数矩阵在一定条件下是可逆的,从而说明四次样条插值函数的存在唯一性。尤其对第一种边界条件,通过差分方程的方法,证明了在等距节点的条件下四次样条插值函数的存在唯一性与插值点数的奇偶性有关。This paper mainly studies the existence and uniqueness of the four times spline interpolation functions.Through giving three boundary conditions and using the thought of three-momene method,we establish the linear equations solving the four times spline interpolation function.When the step length is equal,we study the coefficient matrix of linear equations.Moreover,under the three boundary conditions,we prove that when the coefficient matrix is reversible.Therefore,we prove the existence and uniqueness of the four times spline interpolation function.Especially for the first boundary condition,through the method of differential equation,we prove that the existence and uniqueness of the four times spline interpolation function is relevant with the Odd-Even property of interpolation points number under the condition of the same step length.

关 键 词：样条插值 差分方程 线性方程组 行列式 

分 类 号：O241[理学—计算数学]