逼近已知函数微商的广义Lanczos算法

给出逼近已知函数微商的广义Lanczos 算法, 构造了一列逼近算子$D_{h}^{n}$以提高稳定近似解的收敛速率. 当$n=2$时, 逼近精度达到$O(\delta^{6 \over 7})$, 而对一般的自然数$n$逼近精度为$O(\delta^{\frac{2n+2}{2n+3}})$, 这里$\delta$是近似函数的误差界.

GENERALIZED LANCZOS' ALGORITHM TO APPROXIMATE DIFFERENTIATION OF GIVEN FUNCTIONS

In this paper, a new generalized Lanczos' algorithm to approximate the differentiation of given functions is given. A sequence of operators $D^n_h$ is constructed to improve the convergence rate of the stable approximate solution. For $n=2$, the improved estimate can reach to $O(\delta^{\frac{6}{7}})$, and for general natural number $n$, the rate is $O(\delta^{\frac{2n+2}{2n+3}})$, where $\delta$ is the error bounds of the approximate functions.