0)(x-xk+1)+yk (x-xk-1)(x-xk+1) 2 k+1 )(x-x∠1)(xk-x1) X-x X-x +yk4(xk+1-x1)(x k k=1,2…,n-1 k+1-X 上式称为分段二次 Lagrange插值 若x*为插值点,且x*∈[x,x+1 显然插值区间[xk1,xk41]和xx2]都包含x 那么y=2(x)还是y*=+1(x( )( ) ( )( ) 1 1 1 1 1 - - + + - - - - - = k k k k k k k x x x x x x x x y k = 1,2,L,n - 1 ( ) ( ) 2 L x k ( )( ) ( )( ) 1 1 1 1 - + - + - - - - + k k k k k k k x x x x x x x x y ( )( ) ( )( ) 1 1 1 1 1 k k k k k k k x x x x x x x x y - - - - + + - + - + 上式称为分段二次Lagrange插值 * , * [ , ] Î k k +1 若x 为插值点 且x x x 显然,插值区间 [ , ] [ , ] k -1 k +1 k k +2 x x 和 x x 都包含x * * ( *) ( ) 2 y L x k 那么 = * ( *) ( 1) 2 y L x k + 还是 =