f(x)=f(xo)+fxo,xl(x-xo)+fxo,x,x2l(x-xo)(x-x)+. +fxo2.xn).(xxn1) 由上述差商表对角线上取得的值 f(x)=0, f[xo,x]=-5, f[x0,x,2]=2,f[x0,x1,x2,x3]=1, 则牛顿三次插值多项式为 Nn(x)=0-5(x-1(x-2)(x-3)+2(x-1(x-2) +(x-10(x-2)(x-3) =x3-4x+3.由上述差商表对角线上取得的值 ( 0 0 1 ) 0 1 2 0 1 2 3 0, [ , ] 5, [ , , ] 2, [ , , , ] 1, f x f x x f x x x f x x x x = = − = = ( ) ( )( )( ) ( )( ) ( )( )( ) 3 0 5 1 2 3 2 1 2 1 2 3 4 3. N x x x x x x n x x x x x = − − − − + − − + − − − = − + ( ) ( ) [ , ]( ) [ , , ]( )( ) . f x = f x0 + f x0 x1 x − x0 + f x0 x1 x2 x − x0 x − x1 + [ , . , ]( ).( ) + x0 xn x − x0 x − xn−1 f 则牛顿三次插值多项式为