Hermite插值方法

1、数值分析实验报告五一、 实验目的理解Hermite插值方法，掌握Hermite插值算法设计二、 实验内容使用vc+编程，实现该方法，即Hermite插值法三、 实验步骤#include double herm(double x0,double x1,double y0,double y1,double h0,double g0,double g1,double x)double alp0,alp1,bta0,bta1,t;double s;t=h0*h0;alp0=(x-x1)*(x-x1)*(h0+2*(x-x0)/t/h0;alp1=(x-x0)*(x-x0)*(h0-2*(x-x1)/t

2、/h0;bta0=(x-x0)*(x-x1)*(x-x1)/t;bta1=(x-x1)*(x-x0)*(x-x0)/t;s=y0*alp0+y1*alp1+g0*bta0+g1*bta1;return(s);void main()int n=7;double p0;double pn; double aa8,bb8,s=0;double xx8=0.5,0.7,0.9,1.1,1.3,1.5,1.7,1.9; double yy8=0.4794,0.6442,0.7833,0.8912,0.9636,0.9975,0.9917,0.9463; double g8;int i;double a8

3、,c8,h8;coutPlease input p0 and pnp0;cinpn;for(i=0;i=n-1;i+)hi=xxi+1-xxi;couthi=hiendl;c0=1;g0=3*(yy1-yy0)/h0-p0*h0/2;for( i=1;i=n-1;i+)ai=hi/(hi+hi-1);ci=1-ai;for(i=1;in;i+)coutai=aiendl;coutci=ciendl;for( i=1;i=n-1;i+)gi=3*(ci*(yyi+1-yyi)/hi+ai*(yyi-yyi-1)/hi-1);an=1;gn=3*(yyn-yyn-1)/hn-1+pn*hn-1/2

4、;for(i=0;i=n;i+)coutgi=giendl;aa0=2;bb0=c0/aa0;g0=g0/aa0;for(i=1;i=0;i-)gi=gi-bbi*gi+1;coutendl;for(i=0;i=n;i+)coutgi=giendl;double ss;double c0,c1,d0,d1,g0,g1,h1;double x0;coutPlease input interpolation point x0:x0;if(x0=0.5 & x00.7)c0=xx0;c1=xx1;d0=yy0;d1=yy1;h1=h0;g0=g0;g1=g1;ss=herm(c0,c1,d0,d1,

5、h1,g0,g1,x0);coutss=0.7 & x00.9)c0=xx1;c1=xx2;d0=yy1;d1=yy2;h1=h1;g0=g1;g1=g2;ss=herm(c0,c1,d0,d1,h1,g0,g1,x0);coutss=0.9 & x0=1.1)c0=xx2;c1=xx3;d0=yy2;d1=yy3;h1=h2;g0=g2;g1=g3;ss=herm(c0,c1,d0,d1,h1,g0,g1,x0);coutss=1.1 & x0=1.3)c0=xx3;c1=xx4;d0=yy3;d1=yy4;h1=h3;g0=g3;g1=g4;ss=herm(c0,c1,d0,d1,h1,g0,g1,x0);coutss=1.3 & x0=1.5)c0=xx4;c1=xx5;d0=yy4;d1=yy5;h1=h4;g0=g4;g1=g5;ss=herm(c0,c1,d0,d1,h1,g0,g1,x0);coutss=1.5 & x0=1.7)c0=xx5;c1=xx6;d0=yy5;d1=yy6;h1=h5;g0=g5;g1=g6;ss=herm(c0,c1,d0,d1,h1,g0,g1,x0);coutss=1.7 & x0=1.9)c0=xx6;c1=xx7;d0=yy6;d1=yy7;h1=h6;g0=g6;g1=g7;ss=herm