复平面上广义有理Newton插值的误差公式

Error Formula of Generalized Rational Newton Interpolation on complex plane

1981年,徐利治和杨家新证明了一类广义Newton插值级数可以表示所有有理函数,并在一定条件限制下给出了复数域上的收敛性定理.1986年,徐利治和何天晓将其推广到多元(实或复)的情形,给出了Newton-Lagrange型、Newton-Hermite型及Hermite-fejer型有理插值公式,但是以上都没有给出插值的误差公式.我们对这一问题进行了研究,给出了复平面上一类广义有理Newton插值的误差公式,对复平面上有n+1个极点的亚纯函数该公式仍然成立.

In 1981, Xu Li-zhi and Yang Jia-xin proved that a class generalized Newton interpolation progression can cover all the rational function and converge theory under certain conditions. In 1986, Xu Lizhi and He Tian-xiao set up formulas of rational Newton-Lagrance type, NewtonHermite type and hermite fejer type with above conclusion applied to multi-function （real or complex）. However, all the above are failed to give error formula of interpolation. In the paper a error formula of the generalized rational Newton interpolation on complex plane is given, which fitted for meromorphic function with （n ＋ 1） poles.