| 具调节因子Hermite拟谱逼近的误差估计 |
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| 引用本文： | 赵廷刚.具调节因子Hermite拟谱逼近的误差估计[J].数学杂志,2009,29(1). |
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| 作者姓名： | 赵廷刚 |
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| 作者单位： | 兰州城市学院数学系,甘肃,兰州,730070;上海大学理学院,上海,200444 |
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| 摘 要： | 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.
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| 关 键 词： | Scaled Hermite多项式 求积公式 拟谱逼近 |
ERROR ESTIMATE FOR SCALED HERMITE PSEUDO-SPECTRAL APPROXIMATIONS |
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| ZHAO Ting-gang.ERROR ESTIMATE FOR SCALED HERMITE PSEUDO-SPECTRAL APPROXIMATIONS[J].Journal of Mathematics,2009,29(1). |
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| Authors: | ZHAO Ting-gang |
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| Abstract: | 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. |
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| Keywords: | Scaled Hermite polynomials quadrature formula pseudo-spectral approximation |
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