1.求n次近似多项式pn(x),要求 P,(ro)=f(o), pn(xo=f(xo),, Pn(o)=f(n(xo 令Pn(x)=a0+a1(x-x0)+a2(x-x0)2+…+an(x-x0 则pn(x)= a1+2a2(x-x0)+…+nan(x-x0) X a2+…+n(n-1)an(x-x pm( ao=p2(x0)=f(x0), a1=pn(xo)=f(xo) Pm(x0)=1f"( 0 故Pn(x)=f(x)+f(x0)(x-x0)+2f(x0(x-x0)2+ ni f(xo( 。8 机动目录上页下页返回结束1. 求 n 次近似多项式 要求: ( ) 2! 0 1 2 a p x n =  ( ), 0 = f  x  , ( ) 0 ( ) ! 1 a p x n n = n n ( ) 0 ( ) f x n = 故 pn (x) = ( )0 f x ( )( ) 0 0 + f  x x − x + 2 ! 1 ! 1 n n n f (x )(x x ) 0 0 ( ) + − ! 1 n 2 0 0 + f (x )(x − x ) 2 ! 1 机动 目录 上页 下页 返回 结束 令 pn (x) = 则 pn  (x) = pn (x) =  n an = ! ( ) ( ) p x n n ( ) 0 0 a p x = n ( ), 0 = f x ( ) 1 0 a p x n =  ( ), 0 = f  x a1 2 ( ) 2 0 + a x − x 1 0 ( ) − + + − n n  na x x 2 2!a 2 0 ( 1) ( ) − + + − − n n  n n a x x a0 n n a (x x ) a (x x ) a (x x ) 0 2 + 1 − 0 + 2 − 0 ++ −