82 Newton's Interpolation 牛顿插值/ Newton' s Interpolation N(x)=a0+a1(x-x0)+a2(x-x0(x-x1)+…an(x-x0)…(x-xn1) f(=f(o)+(x-xoflx,xol fx,xo=fo,x,+(x-xuflx,xo,cI 2 fMo,,xu+(x-xunflx,xo ①+(x-x)x②+……+(x-x)…(x-xn-)×(mD f(x)=f(x)+∫x,x1(x-x)+∫x,x1,x2l(x-x0)(x-x1) (+ fIxo,,xmIx-xo)(x-xn-1) fx,x0,…,xnl(x-x)…(x-xn1)(x f[x0,…,x; Rn(r)§2 Newton’s Interpolation  牛顿插值 /* Newton’s Interpolation */ ( ) ( ) ( ) [ , ] 0 0 x x0 f x  f x  x  x f [ , ] [ , ] ( ) [ , , ] 0 0 1 1 0 1 f x x  f x x  x  x f x x x [ , , ..., ] [ , ..., ] ( ) [ , , ..., ] 0 n 1 0 n n x x0 xn f x x x  f x x  x  x f  ( ) ( ) ( )( ) ... ( )...( ) Nn x a0 a1 x x0 a2 x x0 x x1  an x x0 x xn1 1 2 … … … … n1 1 + (x  x0)  2 + … … + (x  x0)…(x  xn1)  n1 ( ) ( ) [ , ]( ) [ , , ]( )( ) ... f x  f x0  f x0 x1 x  x0  f x0 x1 x2 x  x0 x  x1  [ , ... , ]( )...( )  0 n  0  n1 f x x x x x x [ , , ... , ]( )...( )( ) 0 n 0 n 1 n  f x x x x  x x  x x  x  Nn (x) Rn (x) ai = f [ x0 , …, xi ]