| 谱方法的广义Hermite逼近 |
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| 引用本文： | 赵廷刚.谱方法的广义Hermite逼近[J].兰州大学学报(自然科学版),2007,43(1):116-118. |
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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 730000;上海大学理学院,上海 200444 |
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| 摘 要： | 将古典的Hermite多项式推广到广义的形式,并讨论了利用广义的Hermite多项式作为基函数的谱方法的逼近性质.跟古典的Hermite多项式相比,广义的Hermite多项式有更好的逼近性质,而且能够更广泛地适应各种不同的问题.另外还讨论了广义的Hermite函数逼近.
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| 关 键 词： | Hermite多项式 Hermite函数 正交投影 误差估计 |
| 文章编号： | 0455-2059（2007）01-0116-03 |
| 修稿时间： | 2005-05-172006-10-19 |
Generalized Hermite approximations for spectral methods |
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| ZHA Ting-gang.Generalized Hermite approximations for spectral methods[J].Journal of Lanzhou University(Natural Science),2007,43(1):116-118. |
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| Authors: | ZHA Ting-gang |
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| Institution: | 1. Department of Mathematics, Lanzhou City College, Lanzhou 730070, China; 2. Science College, Shanghai University, Shanghai 200444, China |
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| Abstract: | In this paper, the generalized Hermite polynomials are considered for spectral methods. Error estimates for the generalized Hermite approximations are derived in the weighted Sobolev spaces. Compared with the classical Hermite approximation, better approximation properties and more widely application have been achieved. Moreover, the generalized Hermite function approximations are also considered. |
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| Keywords: | Hermite polynomial Hermite function orthogonal projection error estimate |
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