用于积分方程解的广义逆函数值Padé逼近的ε-算法和η-算法

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基金项目: 国家自然科学基金资助项目(10271074)

Epsilon-Algorithm and Eta-Algorithm of Generalized Inverse Function-Valued Padé Approximants Using for Solution of Integral Equations

1.
Department of Mathematics, Shanghai University, Shanghai 200436, P. R. China;
2.
Department of Mathematics, Tongji University, Shanghai 200331, P. R. China

摘要: 为加速具有函数值系数的幂级数收敛并估计积分方程的特征值,建立了两个计算广义逆函数值Padé逼近的有效的递推算法:ε-算法和η-算法.借助于这两个算法之间的内在关系,给出了广义逆函数值Padé逼近的著名的Wynn恒等式.
- 广义逆 /
- 函数值Padé逼近 /
- ε-算法 /
- η-算法 /
- 积分方程
Abstract: Two efficient recursive algorithms epsilon-algorithm and eta-algorithm are introduced to compute the generalized inverse function-valued Pad approximants. The approximants were used to accelerate the convergence of the power series with function-valued coefficients and to estimate characteristic value of the integral equations. Famous Wynn identification of the Padé approximants is also established by means of the connection of two algorithms.
- generalized inverse /
- function-valued Padé approximant /
- epsilon-algorithm /
- eta-algorithm /
- integral equation

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