广义Hermite逼近及基于广义Hermite多项式变换的实现

Generalized Hermite Approximations and Their Implement Based on Generalized Hermite Polynomials Transformation

讨论了利用广义的H erm ite多项式作为基函数的谱方法的逼近性质.和古典的H erm ite多项式相比,广义的H erm ite多项式具有更好的逼近属性和更灵活的适应性.并推导了相应的广义H erm ite多项式变换.利用广义H erm ite多项式变换可以有效地实现广义的H erm ite多项式逼近.数值试验进一步验证了理论的正确性.

The generalized Hermite polynomials are considered as spectral methods. Error estimates for the generalized Hermite approximations are derived in the weighted Sobolev spaces. Compared with the classical Hermite approximation, the generalized ones have better approximation properties and are more flexible for applications. Moreover, the generalized Hermite polynomial transformations are also made in order to implement the projection. Numerical tests verify the theoretical results.