Chapter 2 插值方法 :当n=1时,满足插值条件 H3(×)=f(X),H3(x)=f(×),i=0,1 的插值公式: a()=(1+20)),a(x)=1+2x)(), x X-X 风(x)=(x-x))2 β(x)=(x-x) x0-x1 11-x0 H3(x)=f()a(x)+f(x)01(x)+f(x)6(x)+f(x)(x) R(x)=f(x)=H3(x) (ξ) 4! (x-x)(x-x)2x<5<x 应HUST注:当n=1时 满足插值条件 H3(xi)=f(xi) Hí3(xi)=fí(xi) i=0,1 的插值公式: x x x x x xx xx 0 1 2 0 10 01 - - ( ) =(1+2 )( ) , - - α x x x x x xx xx 1 0 2 1 01 10 - - ( ) =(1+2 )( ) , - - α x x x xx x x 1 2 0 0 0 1 - ( ) =( - )( ) , - β x x x xx x x 0 2 1 1 1 0 - ( ) =( - )( ) , - β H x fx x fx x f x x f x x 3 00 11 0 0 11 ( ) = ( ) ( )+ ( ) ( )+ '( ) ( )+ '( ) ( ). αα β β f R x f x Hx xx xx x x (4) 2 2 3 3 0 10 1 ( ) ( )= ( )= ( )= ( - ) ( - ). < < . 4!ξ ξ