对含有不可达点的有理插值函数的研究  

Study of rational interpolation function with unattainable points

作　　者：李慷慨[1] 朱晓临[1] 李勇[1] 郑剑平[1] 

机构地区：[1]合肥工业大学数学学院,安徽合肥230009

出　　处：《合肥工业大学学报（自然科学版）》2010年第6期922-924,共3页Journal of Hefei University of Technology：Natural Science

基　　金：国家自然科学基金资助项目(60473114);安徽省自然科学基金资助项目(070416227)

摘　　要：文章从正向和倒向2个方面给出了2个判别有理插值函数的不可达点的定理。在判断出相应的有理插值函数含有不可达点时,构造了一种混合有理插值函数满足所有的插值条件。所得混合有理插值函数比以往同类方法得到的混合有理插值函数的分子、分母次数低,而且计算量小,所得算法简便、可操作性强,易于编程。文章还通过数值例子具体说明了上述方法。This paper presents two theorems for testing whether a rational interpolation function has any unattainable point（s） from the forward and backward method. In the case that the rational inter- polation function has unattainable point（s）, a kind of blending rational interpolation is constructed to change the unattainable point（s） into the attainable one（s）. Compared with the previous ones, the de- grees of the numerator and denominator of the blending rational interpolation introduced in this paper are lower. Consequently, the computation is much less. In addition, the algorithm for the above method is simple and easy to program. Some numerical examples are given to clarify the method.

关 键 词：Thiele-Werner型有理插值 不可达点 混合有理插值 

分 类 号：O241.5[理学—计算数学]