函数值Padé逼近的一种新的行列式表示及其应用  

A new determinantal representation for function-valued Padé approximant and its application

作　　者：李勇[1] 朱晓临[1] 郑剑平[1] 李慷慨[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918-921,共4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：文章将函数值Padé逼近问题转化为以数量为分量的向量值Padé逼近问题,构造了函数值Padé逼近的一种新的行列式表示,其元素只需向量间的点乘运算,而传统的行列式表示中每个元素都是通过求定积分得到的,因此文中的行列式表示计算量大大减少。此外,文中还将上述方法应用到第2类Fredholm积分方程求解问题上,并给出数值例子显示其具有很好的逼近效果。This paper constructs a new determinantal representation for function-valued Pade approxi- mation by converting function-valued Pade approximation into vector-valued Pade approximation with scalar components. Each element of the determinant is obtained by the operation of dot product of two vectors rather than by evaluating a definite integral of a function traditionally. So the calculation a- mount of the determinant introduced in the paper is much less than the traditional one. In addition, this method is also used to find the numerical solution of Fredholm integral equation of the second kind. Numerical examples show the good approximate accuracy of the method.

关 键 词：函数值Padé逼近 向量值Padé逼近 行列式表示 第2类Fredholm积分方程 

分 类 号：O241.5[理学—计算数学]