基于Pade逼近的广义Lagrange混合有理插值

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。

Generalized Lagrange Blending Rational Interpolation Based on Pade Approximation

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.