三次样条插值 S(x)={s(x),x∈[x12x 1)S;(x)=c1x+bx2+C1+d1(i=1,…n) 2)S(x1)=v1(i=0,1,…n) 3)S(x)∈C[x,x] →s(x)=S(x),s(x)=s1(x)2s"x)=sm1(x)(i=1…,n-1) 4)S"(x0)=S"(xn)=0(然边界条件) 2)3)4) b S lim s(x)=g(x) n→0 g(x)为被插值函数。三次样条插值 ( ) { ( ), [ , ], 1, } S x = si x x xi−1 xi i = n 3) ( ) [ , ] 2) ( ) ( 0,1, ) 1) ( ) ( 1, ) 0 2 3 2 n i i i i i i i S x C x x S x y i n s x a x b x c x d i n  = = = + + + =   ( ) ( ), ( ) ( ), ( ) ( ) ( 1, , 1)  si xi = si+1 xi si  xi = si  +1 xi si  xi = si  +1 xi i =  n − 4) S(x0 ) = S(xn ) = 0 (自然边界条件） 2) 3) 4) a ,b ,c ,d S(x)  i i i i  g(x)为被插值函数。 lim ( ) ( ) n S x g x → =