L(x)=y/l(x)+y+1k1(x) k=0,1,…,n-1 X-x k+1 X-X X-x k+1 k+1 k L(x)x0≤x<x1 (x)x1≤x<x2 -(2) (x)xn1≤x≤xn 显然 (x1)=y,i=0,1 我们称由(1)2)式构成的插值多项式L1(x)为 分段线性 Lagrange插值多项式( ) ( ) ( ) 1 1 ( ) 1 L x y l x y l x k k k k k = + + + 1 1 + + - - = k k k k x x x x y k k k k x x x x y - - + + + 1 1 k = 0,1,L, n - 1 L1 (x) = ï ï î ï ï í ì £ £ £ < £ < - - n n n L x x x x L x x x x L x x x x 1 ( 1) 1 1 2 (1) 1 0 1 (0) 1 ( ) ( ) ( ) M M 显然 L1 (xi ) = yi , i = 0,1,L,n --------(1) --------(2) 我们称由(1)(2)式构成的插值多项式 为 分段线性Lagrange插值多项式 ( ) 1 L x