Chapter 2 插值方法 例题25依据下列数据表构造插值多项式 X YY 解 003 H3(x)=00(x)+101(x)+3B(x)+96(x) X x (1+2)( -)2+3(x-0)()2+9(x-1)( 0-10-1 0-1 2 2x3+3x2+3x(x2-2x+1)+9x2(x-1) 10x3-12x2+3x (E R3(x) x x 4! 0<5<1 and depending on x 应HUST例题2.5 依据下列数据表构造插值多项式 1 1 9 3 Y’ 0 0 X Y 解: Hx x x x x iii 3 0 1 01 ( )=0 ( )+1 ( )+3 ( )+9 ( ) α α ββ xx x x x x 2 22 -1 -0 -1 -1 = (1+ 2 )( ) + 3( - 0)( ) + 9( -1)( ) 0-1 0-1 0-1 0-1 x x xx x x x 32 2 2 = -2 + 3 + 3 ( - 2 +1) + 9 ( -1) x xx 3 2 = 10 -12 + 3 f Rx x x , (4) 2 2 3 ( ) ( ) = ( - 0) ( -1) 4!ξ 0< <1 . ξ and depending on x