) 中图学技术大荸学系 University of Science and Technology of China DEPARTMENT OF MATHEMATICS Newton型多项式插值 承袭性:Nn1(x)=Nn(x)+qn1(x)∈P" 051 + h N,()=Mn+(x=f(x) gm(x)=a21(x-x)…(x-xn)为实数 同样Nn(x)=Mn1(x)+qn(x) →qn(x)=an2(x-x0)…(x-xn21)数 学 系 University of Science and Technology of China DEPARTMENT OF MATHEMATICS Newton型多项式插值 {x0 , x1  , xn+1 } {x0 , x1  , xn } 且 Nn (xi ) = Nn+1 (xi ) = f (xi ) , i =1, n ( ) ( ) ( ) n 1 n 1 0 n q x = a x − x x − x + +  同样 ( ) ( ) ( )  n = n − 0 − n−1 q x a x x  x x ( ) ( ) ( ) 1 N x N x q x n = n− + n 承袭性： ( ) ( ) ( ) 1 1 N x N x q x n+ = n + n+ +1  n P 为实数