中文摘要：

提出一种基于广义Hermite函数展开的谱方法和拟谱（广义Hermite—Gauss插值）方法，获得相应近似导数的收敛性估计。理论分析表明，此方法有着与ZHAO（2011年）中同样的收敛速度，但通过适当的选取广义Hermite函数中的尺度因子α，可以大大降低投影空间基底的个数，从而提高了计算效率。

英文摘要：

Spectral and pseudospectral （generalized Hermite-Gauss Interpolation） methods are proposed based on generalized Hermite functions, thereby the convergence estimate of the corresponding approximate derivative is obtained. The theoretical analysis indicates that the proposed methods have the same convergence rates as one in ZHAO＇ s paper （2011）. However, the number of basis functions of the pro- jection space can be significantly reduced by choosing properly the scaling factor c- in generalized Hermite function, thus the computational efficiency of the methods is improved.