Chapter 2 Hermite插值 插值方法 Problem:已知f(x),f(X),i=01,…n.求H2n+1(×) H2n+(X)=f(×),H2n+12(X)=f(x),i=01,2…n 基函数法: (1)2n+2个已知量f(x)f(X),i=0,1,2,…n (2)构造2+2个基函数a(x)β(×),i=0,12,n (3)使H2n+1()为2n+2个基函数的线性组合: 2n+1-00(X)()+a (X)f(×1)+…+an(x)f(xn +β0(Xf(x)+B1(×)f(x1)+…+Bn(X)f(x) 如何求这些基函数呢? 应HUSTHermite插值 Problem: 已知f(xi) f’(xi) i=0,1,…n.求H2n+1(x) H2n+1(xi)=f(xi), H2n+1’(xi)=f’(xi), i=0,1,2,…n. 基函数法 1 2n+2个已知量f(xi), f’(xi) i=0,1,2,…n. 2 构造2n+2个 基函数 i(x), i(x) i=0,1,2,…n. 3 使H2n+1(x)为2n+2个基函数的线性组合 H2n+1= 0(x)f(x0)+ 1(x)f(x1)+…+ n(x)f(xn) + 0(x)f’(x0)+ 1(x)f’(x1)+…+ n(x)f’(xn). 如何求这些基函数呢?