) 中图学技术大荸学系 University of Science and Technology of China DEPARTMENT OF MATHEMATICS 误差R,(x)=f(x)-Ln(x) 解 f(x1)=Ln2(x),i=0,…n . R n (x1)=0,i=0, R,(x)=k(x(x-xo).(x-xn) 求k(x)=? Va,k(a=? 设v(t)=f(1)-Ln()-k(a)(t-x)…(t-xn) 易知v(x)=0,i=0,… n and y(a)=0数 学 系 University of Science and Technology of China DEPARTMENT OF MATHEMATICS 误差 R (x) f (x) L (x) n = − n 解： ( ) ( )( ) ( ) ( ) 0 , 0, ( ) ( ) , 0, n 0 n n i i n i R x k x x x x x R x i n f x L x i n  = − −  = = = =     求 k(x) = ? ( ) 0, 0, and ( ) 0 ( ) ( ) ( ) ( )( ) ( ) , ( ) ? 0 = = = = − − − −  = x i n a t f t L t k a t x t x a k a i n n     设  易知