保导函数的无穷极限的向量值连分式插值  

Vector-valued Continued Fraction Interpolation of Preserving Infinite Limit of the Derivative Function

作　　者：赵前进 吴开文 ZHAO Qianjin;WU Kaiwen(School of Mathematics and Big Data,Anhui University of Science and Technology,Huainan Anhui 232001,China)

机构地区：[1]安徽理工大学数学与大数据学院,安徽淮南232001

出　　处：《安徽理工大学学报（自然科学版）》2022年第4期90-95,共6页Journal of Anhui University of Science and Technology:Natural Science

基　　金：国家自然科学基金资助项目(60973050)。

摘　　要：针对传统的Thiele型向量值连分式插值的导函数有无穷极限时无法保持原有的无穷极限这一问题,基于倒差商与连分式插值函数分子多项式和分母多项式的首项系数的恒等关系,构建了保导函数的无穷极限的向量值连分式插值算法,证明了保导函数的无穷极限的向量值连分式插值这一数值问题的存在性及唯一性,给出了误差分析并通过数值例子证明了新算法的有效性。新的插值方法构建了逼近效果更好的插值函数,在某些实际问题中,提供了新的思路。The vector-valued rational interpolation based on the classical Thiele-type vector-valued continued fractions cannot maintain the infinite limit of the derivative function when the derivative function of the interpolated function is of infinite limits.To this problem,the novel algorithm for the vector-valued continued fraction interpolation was constructed by means of the relationship between the reciprocal differences and the leading coefficients of the numerator and the denominator of the vector-valued continued fraction interpolation in an effort to preserve the infinite limit of the derivative function while approximating the given function with the infinite limit of the derivative function.The uniqueness of the interpolation problem was proved with numerical examples given to verify the effectiveness of the presented algorithm.The new interpolation method constructs interpolation function with better approximation effect and provides a new idea in some practical problems.

关 键 词：向量值有理插值 保无穷极限 倒差商 逆差商 导函数 

分 类 号：O241.5[理学—计算数学]