中图苔技术大荸数学系 University of Science and Technology of China DEPARTMENT OF MATHEMATICS 中心差商 f(x0+h)-f(x0-h) 2h 由 Taylor展开 h f(xo+h)=f(o)+hf(xo)+af(xo)+af (s,xo sssxo +h 2 f(x。-h)=f(x0)-h(x0)+f"(x0)-f"(52),x-h≤52≤x 因此,有误差 R(x)=f(x0) (xo+h)-f(o-h) 2h I八"(1)+f"(2)=f"(5)=O(h2)数 学 系 University of Science and Technology of China DEPARTMENT OF MATHEMATICS h f x h f x h f x 2 ( ) ( ) '( ) 0 0 0 + − −  由Taylor展开 2 3 0 0 0 0 1 0 1 0 2 3 0 0 0 0 2 0 2 0 ( ) ( ) '( ) ''( ) '''( ), 2! 3! ( ) ( ) '( ) ''( ) '''( ), 2! 3! h h f x h f x hf x f x f x x h h h f x h f x hf x f x f x h x     + = + + +   + − = − + − −   因此，有误差 '''( ) ( ) 6 [ '''( ) '''( )] 12 2 ( ) ( ) ( ) '( ) 2 2 1 2 2 0 0 0 f O h h f f h h f x h f x h R x f x = + = = + − − = −    中心差商