H3()=yao(x)+yai()+yP(x)+yiB(x) 其中 (x)=1aa(x1)=0ka(x)=0a(x1)=0 a1(x)=0g(x)=1a(x)=0a(x)=0 B(x)2=0B6(x)=0(x)=1B(x)=0 B1(x)2=0B1(x)2=0B(x)=0-(x)=1 可知x1是a(x)的二重零点,即可偎设 a0(x)=(x-x1)2(ax+b) 由 (x)=0
其中 ( ) 1 a0 x0 = ( ) 0 b0 x0 = ( ) 1 b0 ¢ x0 = ( ) ( ) ( ) ( ) ( ) 3 0 0 1 1 0 0 1 1 H¢ x = y a¢ x + y a¢ x + y ¢b¢ x + y ¢b¢ x ( ) 0 a0 x1 = ( ) 0 a1 x0 = ( ) 1 a1 x1 = ( ) 0 b0 x1 = ( ) 0 b1 x0 = ( ) 0 b1 x1 = ( ) 0 a0 ¢ x0 = ( ) 0 a0 ¢ x1 = ( ) 0 a1 ¢ x0 = ( ) 0 a1 ¢ x1 = ( ) 0 b0 ¢ x1 = ( ) 0 b1 ¢ x0 = ( ) 1 b1 ¢ x1 = 可知 x1是a0 (x)的二重零点,即可假设 ( ) ( ) ( ) 2 0 1 a x = x - x ax + b ( ) 1 a0 x0 = ( ) 0 由 a0 ¢ x0 =
可得 b )2(x0-x1) (x)=(x-x1)2(ax+b) 2x 1 0 3 0 0 (x-x1) 2x0 2x agrange 0 0 1 插值基函数 X-x 1+2 (1+2l(x):l2(x) X-x
可得 3 0 1 ( ) 2 x x a - = - 3 0 1 0 2 0 1 ( ) 2 ( ) 1 x x x x x b - + - = ( ) ( ) ( ) 2 0 1 a x = x - x ax + b 2 1 = (x - x ) ç ç è æ - - 3 0 1 ( ) 2 x x x ÷ ÷ ø ö - + - + 3 0 1 0 2 0 1 ( ) 2 ( ) 1 x x x x x 2 0 1 2 1 ( ) ( ) x x x x - - = ÷ ÷ ø ö - - 0 1 2 x x x ç ç è æ - + 0 1 2 0 1 x x x ÷ ÷ ø ö ç ç è æ - - = + 1 0 0 1 2 x x x x 2 0 1 1 ÷ ÷ ø ö ç ç è æ - - x x x x (1 2 ( )) ( ) 2 1 0 = + l x ×l x Lagrange 插值基函数