P(x)应满足插值条件P(x)=f,i=0,1…,n 有P(x)=f P(x1)=f1=ao+a1(x1-x0) P(x2)=f2=ao+an1(x2-x)+a2(x2-x)(x2-x1) f2-fo fi-fo x2-x0x1-x0 再继续下去待定系数的形式将更复杂 为此引入差商和差分的概念P(x)应满足插值条件 P(xi ) = f i , i = 0,1,L,n 0 0 0 有 P(x ) = f = a ( ) ( ) 1 1 0 1 1 0 P x = f = a + a x - x 0 0 a = f 1 0 1 0 1 x x f f a - - = ( ) ( ) ( )( ) 2 2 0 1 2 0 2 2 0 2 1 P x = f = a + a x - x + a x - x x - x 2 1 1 0 1 0 2 0 2 0 2 x x x x f f x x f f a - - - - - - = 再继续下去待定系数的形式将更复杂 为此引入差商和差分的概念