用于积分方程解的函数值Padé-型逼近的正交多项式和行列式公式  

Orthogonal Polynomials and Determinant Formulas of Function-Valued Padé-Type Approximation Using for Solution of Integral Equations

作　　者：顾传青[1] 潘宝珍[1] 吴蓓蓓[1] 

机构地区：[1]上海大学数学系,上海200444

出　　处：《应用数学和力学》2006年第6期750-756,共7页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(10271074)

摘　　要：为了求解第二类Fredholm积分方程,引入了一个广义线性泛函,从而定义了一种新的函数值Padé_型逼近.借助于积分方程解的幂级数展开式,这种逼近方法可用来构造积分方程的近似解.定义了Padé_型逼近的正交多项式,在此基础上给出了两种形式的实用的分子行列式和分母行列式公式.To solve Fredholm integral equations of the second kind, a generalized linear functional is introduced and a new function-valued Padé-type approximation was defined. By means of the power series expansion of the solution, this method can construct an appoximate solution to solve the given integral equation. On the basis of the orthogonal polynomials, two useful deter-minant expressions of the numerator polynomial and the denominator polynomial for Padé-type approximation were explicitly given.

关 键 词：广义线性泛函 函数值 Padé-型逼近 FREDHOLM积分方程 正交多项式 行列式公式 

分 类 号：O241.83[理学—计算数学]