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

基金项目: 国家自然科学基金资助项目(10271074)

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

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．
- 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
Abstract: To solve Fredholm integral equations of the second kind,a generalized linear functional is introduced and a new function-valued Pad-type approximation was defined.By means of the power series expansion of the solution,this method can construct an approximate 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 Pad-type approximation were explicitly given.
- generalized linear functional /
- function-valued /
- Pad-type approximation /
- Fredholm integral equation /
- orthogonal polynomial /
- determinant formula

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