高精度的复合重心有理Hermite插值方法

在插值节点数较多时,有理插值往往比多项式插值具有更好的逼近效果,但是,有理插值难以避免出现极点、难以控制极点的位置,同时也可能出现不可达点.重心有理Hermite插值具有许多优点,如数值稳定性好、可以设法避免不可达点、极点的出现.本文对一元Pade型逼近和重心有理Hermite插值进行复合,构造出了一种新的高精度复合重心有理Hermite插值方法,并给出了数值实例表明新方法具有更高的精度.

Composite Barycentric Rational Hermite Interpolation with High-Accuracy

It is well known that rational interpolation sometimes gives better approximations than polynomial interpolation,especially for large sequences of points,but it is difficult to avoid poles,unattainable points and control the occurrence of poles.Barycentric rational Hermite interpolants possess some advantages,for example,the unwanted unattainable points and poles can be avoided,and good numerical stability can be ensured.In this paper,a new composite barycentric rational Hermite interpolation approach with ...