) 中图学技术大荸学系 University of Science and Technology of China DEPARTMENT OF MATHEMATICS 同样Nn(x)的误差为R2(x)= (x-x)…(x-xn) (n+1) 另一方面 设{x1}20 Newton插值为N(x 则有{x}0∪a}为Nn1(t)=Nn(t)+/[x02…,xn,a](t-x0)…(t-xn 显然Nn1(a)=f(a) 误差 f(a)-Nn(a)=x,,xn,以l(a-x0)…(a-x fTO,.,n, a] f+(与5)「性质3 (n+1)!数 学 系 University of Science and Technology of China DEPARTMENT OF MATHEMATICS 误差 0 0 1 0 0 1 0 0 { } Newton ( ) { } { } ( ) ( ) [ , , , ]( ) ( ) ( ) ( ) ( ) ( ) [ , , , ]( ) ( ) n i i n n i i n n n n n n n n x N x x a N t N t f x x a t x t x N a f a f a N a f x x a a x a x = = + + = + − − =  − = − − 另一方面 设 插值为 则有 为 显然 ( 1)! ( ) [ , , , ] 1 0 +  = + n f f x x a n n   性质3 1 0 ( ) ( ) ( ) ( ) ( ) ( 1)! n n n n f N x R x x x x x n  + = − − + 同样 的误差为