8 1 Lagrange Polynomial The mathematician S had to move to a new place His wife didnt trust him very much, so when they stood down on the street with all their things she asked him to watch their ten trunks, while she got a taxi. Some minutes later she returned. Said the husband: "I thought you said there were ten trunks, but Ive only counted to nine The wife said: "No, they're TEN! But i have counted them :0.1.2 n21希望找到(x),=0,…,n使得();然后令 P(x)=∑l(x)y,则显然有Pn(x)=y2 l(x)每△ ▲ 与节点有关,而与∫无关 Lagrange Polynomial (x2-x;) x-xi (x-x;) (x)=∑l(x)yThe mathematician S. had to move to a new place. His wife didn't trust him very much, so when they stood down on the street with all their things, she asked him to watch their ten trunks, while she got a taxi. Some minutes later she returned. Said the husband: "I thought you said there were ten trunks, but I've only counted to nine!" The wife said: "No, they're TEN!" "But I have counted them: 0, 1, 2, ..." §1 Lagrange Polynomial n  1 希望找到li(x)，i = 0, …, n 使得 li(xj)=ij ；然后令 = = n i n i i P x l x y 0 ( ) ( ) ，则显然有Pn (xi) = yi 。 li(x) 每个 li有 n 个根 x0 … xi … xn  = = - - - = - n j j  i i x Ci x x x xi x xn Ci x xj l 0 ( ) ( 0 )...( )...( ) ( )  - = = j  i i j i i i x x l x C ( ) 1 ( ) 1  =  - - = n j j i i j j i x x x x l x 0 ( ) ( ) ( ) = = n i n i i L x l x y 0 ( ) ( ) Lagrange Polynomial 与 节点 有关，而与 f 无关