当前位置: X-MOL 学术J. Comput. Appl. Math. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
The least-squares fit of highly oscillatory functions using Eta-based functions
Journal of Computational and Applied Mathematics ( IF 2.4 ) Pub Date : 2020-03-06 , DOI: 10.1016/j.cam.2020.112839
S. Mashayekhi , L.Gr. Ixaru

In this paper we examine the possibility of using the Eta functions as a new base for high quality approximations of oscillatory functions with slowly varying weights. We focus on the least squares and piecewise least squares approximation of such functions and compare the results obtained by using Eta-based sets of functions with those obtained by means of the Legendre polynomials and Fourier series. We find out that the accuracies from these are more or less equivalent for small frequencies but they exhibit different behaviors when the frequency is increased: the accuracy worsens for the Legendre polynomials and Fourier series base but it remains bounded for the new base, in accordance with the known properties of the Eta functions. Such an advantage makes the new base quite attractive for being used in many other mathematical contexts where highly oscillatory functions are involved.



中文翻译:

使用基于Eta的函数的高振荡函数的最小二乘拟合

在本文中,我们研究了使用Eta函数作为权重缓慢变化的振荡函数的高质量近似的新基础的可能性。我们关注此类函数的最小二乘和分段最小二乘近似,并将通过使用基于Eta的函数集获得的结果与通过Legendre多项式和Fourier级数获得的结果进行比较。我们发现,对于小频率,这些精度几乎相等,但是当频率增加时,它们表现出不同的行为:勒让德多项式和傅里叶级数基的精度变差,但根据新的基,它仍然限于新基Eta函数的已知属性。

更新日期:2020-03-06
down
wechat
bug