论文标题
高斯波数据包通过正交规则转换
The Gaussian Wave Packet Transform via Quadrature Rules
论文作者
论文摘要
我们分析了高斯波数据包变换。基于由高斯基础函数集合形成的傅立叶反演公式和统一分区，提出了正方形综合函数的新表示。然后，包括严格的误差分析，通过不同的正交规则对傅立叶积分的离散化来得出波数据包变换的变体。基于高斯 - 高矿正流，我们引入了高斯波包的新表示，其中基本函数的数量大大减少。 1D中的数值实验说明了理论结果。
We analyse the Gaussian wave packet transform. Based on the Fourier inversion formula and a partition of unity, which is formed by a collection of Gaussian basis functions, a new representation of square-integrable functions is presented. Including a rigorous error analysis, the variants of the wave packet transform are then derived by a discretisation of the Fourier integral via different quadrature rules. Based on Gauss--Hermite quadrature, we introduce a new representation of Gaussian wave packets in which the number of basis functions is significantly reduced. Numerical experiments in 1D illustrate the theoretical results.
