Journal of Computational and Applied Mathematics ( IF 2.1 ) Pub Date : 2021-03-30 , DOI: 10.1016/j.cam.2021.113569 Ke Jing , Ning Kang
It is well-known that the Floater–Hormann interpolants give better results than other interpolants, especially in the case of equidistant points. In this paper, we generalize it to the Hermite case and establish a family of barycentric rational Hermite interpolants that do not suffer from divergence problems, unattainable points and occurrence of real poles. Furthermore, if the order of the Hermite interpolant is even and , the function converges to the corresponding function at the rate of as the mesh size for , regardless of the distribution of the points; and if the interpolation points are quasi-equidistant and , the function converges to corresponding function at the rate of as for , regardless of the parity of the order of the Hermite interpolant.
中文翻译:
一类重心有理Hermite插值及其衍生物的收敛速度
众所周知,Floater-Hormann插值比其他插值提供更好的结果,尤其是在等距点的情况下。在本文中,我们将其推广到Hermite案例并建立一个重心有理Hermite插值族不会受到发散问题,无法达到的分数和实际极点的困扰。此外,如果订单 Hermite插值的偶数和 , 功能 收敛到相应的功能 以...的速度 作为网眼尺寸 为了 ,无论积分的分布如何;并且如果插值点是准等距的,并且, 功能 收敛到相应的功能 以...的速度 作为 为了 ,而不考虑订单的平价 Hermite插值器。