) 中图学技术大荸学系 University of Science and Technology of China DEPARTMENT OF MATHEMATICS 向后差商 f(o) f(o)-f(xo -h h 由 Taylor展开 h f(x。-h)=f(x)-b(x)+f"(5,x0≤5≤x+h 因此,有误差 R(x)=f(ro)f(xo)-f(xo-h)h =f"()=O(h h数 学 系 University of Science and Technology of China DEPARTMENT OF MATHEMATICS h f x f x h f x ( ) ( ) '( ) 0 0 0 − −  由Taylor展开 f x x h h f x − h = f x − hf x + 0   0 + 2 0 0 0 ''( ), 2! ( ) ( ) '( )   因此，有误差 ''( ) ( ) 2! ( ) ( ) ( ) '( ) 0 0 0 f O h h h f x f x h R x f x = = − − = −  向后差商