C語言編寫牛頓插值多項(xiàng)式的實(shí)現(xiàn)

實(shí)驗(yàn)名稱：Newton插值多項(xiàng)式實(shí)驗(yàn)?zāi)康牧私釴ewton插值多項(xiàng)式實(shí)驗(yàn)類型設(shè)計(jì)型實(shí)驗(yàn)環(huán)境WindowsXPTC實(shí)驗(yàn)內(nèi)容相關(guān)知識(shí)：通過n+1個(gè)節(jié)點(diǎn)的次數(shù)不超過n的Newton插值多項(xiàng)式為：N(x)=f(x)+f[x,x](x-x)+f[x,x,x](x-x)(x-x)+…

n 0 0 1 0 0 1 2 0 1+f[x,x，…，x](x-x)(x-x)…(x-x)01 n 0 1 n-1數(shù)據(jù)結(jié)構(gòu)：兩個(gè)一維數(shù)組或一個(gè)二維數(shù)組算法設(shè)計(jì)：(略)實(shí)驗(yàn)用例：已知函數(shù)y=f(x)的一張表(同上一個(gè)試驗(yàn))試驗(yàn)要求：利用Newton插值多項(xiàng)式n(x)求被插值函數(shù)f(x)在點(diǎn)x=65處的近似值。建議:畫出Newton插值多項(xiàng)式n(x)的曲線。編寫代碼：#include<stdio.h>#include<graphics.h>doubleJuncha(doublea[13][2],intf,intl)(doublem;if((l-f)>1)(m=(Juncha(a,f+1,l)-Juncha(a,f,l-1))/(a[l][0]-a[f][0]);}elsem=(a[l][1]-a[f][1])/(a[l][0]-a[f][0]);returnm;}doubleNewton(doublea[13][2],doublex)(doublem,n,y;inti,j;y=a[0][1];i=j=1;while(i!=13)(j=0;m=n=1.0;m=Juncha(a,j,i);while(j!=i)(n=(x-a[j][0])*n;j++;}y=y+m*n;i++;}returny;}doubleLglr(doublea[13][2],doublex)(doublem,n,y;inti,j;m=n=1.0;i=j=y=0;while(i!=13)j=0;m=n=1;while(j<13)(if(j!=i)m=(x-a[j][0])*m;j++；}j=0；while(j<13)(if(j!=i)n=(a[i][0]-a[j][0])*n;j++；}y=y+m/n*a[i][1];i++;}returny;}voidmain()(doublea[13][2]={0,5,10,1,20,7.5,30,3,40,4.5,50,8.8,60,15.5,70,6.5,80,-5,90,-10,100,-2,110,4.5,120,7};doublex,x1;intarw[6]={515,235,520,240,515,245};intarw1[6]={315,45,320,40,325,45};intgdriver=VGA;intgmode=VGAHI;initgraph(&gdriver,&gmode,"c:\\TC20\\BGI");cleardevice();printf("inputx:\n");scanf("%lf",&x);x1=x;printf("y=%f\n",Newton(a,x));setbkcolor(7);setcolor(14);setlinestyle(0,0,3);drawpoly(3,arw);drawpoly(3,arw1);line(120,240,520,240);line(320,40,320,440);setlinestyle(1,0,1);line(320,150,320,340);line(330,150,330,340);line(340,150,340,340);line(350,150,350,340);line(360,150,360,340);line(370,150,370,340);line(380,150,380,340);line(390,150,390,340);line(400,150,400,340);line(410,150,410,340);line(420,150,420,340);line(430,150,430,340);line(440,150,440,340);setcolor(3);outtextxy(320,30,"Y");outtextxy(310,245,〃O〃)；outtextxy(525,240,〃X〃)；settextstyle(4,0,4);outtextxy(450,400,〃Newton...〃)；x=0;setcolor(2);setlinestyle(0,0,3);moveto((x+320),(240-Newton(a,x)));while(x<=119)(x=x+1;lineto((x+320),(240-Newton(a,x)));}x=0;setcolor(6);setlinestyle(0,0,1);moveto((x+320),(240-Lglr(a,x)));while(x<=119)(x=x+1;lineto((x+320),(240-Lglr(a,x)));}setcolor(4);setlinestyle(1,0,1);line((x1+320),((240-Newton(a,x1))-80),(x1+320),((240-Newton(a,x1)