具调节因子Hermite拟谱逼近的误差估计

摘要

Pseudo-spectral approximation of a function in terms of the scaled Hermite functions in certain weighted Sobolev spaces is analyzed. By using properties of the scaled Hermite polynomials and the corresponding Gauss-type quadrature formula, an stability estimate for the interpolation operator on zeros of the scaled Hermite polynomials is obtained. Also error estimate for the interpolation operator is obtained. The results show that the scaled Hermite pseudo-spectral approximation shares high accuracy.%本文研究了具调节因子的Hermite函数的拟谱方法在赋权Sobolev空间中函数的逼近.通过具调节因子的Hermite多项式的性质和相应的Gauss类型的求积公式,得到了在具调节因子的Hermite多项式的零点上的插值算子的稳定性以及误差界.并具有通常的高阶收敛性.