) 中图学技术大荸学系 University of Science and Technology of China DEPARTMENT OF MATHEMATICS 事后误差估计 给定气任取n+1个构造Ln(x) 如 i=0. → 另取i=1,…,n+1 则 (n+ f(x-L(x)= 1(x-x0)…(x-x,) (n+1) (n+1) f(x)-L,(x)= (x-x1)…(x-xn+1) n+数 学 系 University of Science and Technology of China DEPARTMENT OF MATHEMATICS 事后误差估计 给定   1 0 + = n i i x 任取n+1个构造 L (x) n ( ) ~ 1, , 1 0, , ( ) i n L x i n L x n n = +  =   如：  另取 则 ( ) ( ) ( 1)! ( ) ( ) ~ ( ) ( ) ( ) ( 1)! ( ) ( ) ( ) 1 1 2 ( 1) 0 1 ( 1) + + + − − + − = − − + − = n n n n n n x x x x n f f x L x x x x x n f f x L x    