摘要
Lagrange插值建立在Lagrange插值基函数的基础之上,是一种便于理论分析的多项式插值。将传统的Lagrange插值方法和Pade逼近相结合,构造一种新的混合有理插值。对于每个插值节点处给定的形式幂级数,先在每个插值节点处求得其Pade逼近,然后用Lagrange插值基函数对它们进行加权组合,从而得到一种新的混合有理插值——广义Lagrange混合有理插值。新的混合有理插值方法通过选择每个插值节点处的Pade逼近,可以获得不同的混合有理插值,且包含传统的Lagrange插值作为特例。为了得到更精确的插值,进一步研究了基于Pade型逼近和基于扰动Pade逼近的混合有理插值。给出的数值例子表明了新方法的有效性。
Lagrange＇s polynomial interpolation based on Lagrange＇s basis functions, is a polynomial interpolation convenient for theoretic analysis. A kind of blending rational interpolants was constructed by combination of traditional Lagrange＇s interpolation and Pade approximation. For a given formal power series at every interpolation node, a Pade approximant was made and then they were blended by means of Lagrange interpolating basis functions to form a new blending rational interpolation-generalized Lagrange blending rational interpolation. Different blending rational interpolants including classical Lagrange＇s polynomial interpolation as their special case can be obtained by the new blending rational in- terpolation method with selecting Pade approximant at each interpolation node. In order to obtain more accurate interpolation, Pade-type approximation based blending rational interpolation and perturbed Pad6 approximation based blending rational interpolation were studied. Given numerical examples indicated the validity of the new method.
出处
《安徽理工大学学报（自然科学版）》
CAS
2010年第1期68-72,共5页
Journal of Anhui University of Science and Technology:Natural Science
基金
国家自然科学基金资助项目(60973050)
安徽省教育厅自然科学基金资助项目(KJ2009A50
KJ2007B173)
