《数值分析》上机习题

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1、《数值分析》上机习题1.用Newton法求方程X7-28X4+14=0在(0.1,1.9)中的近似根(初始近似值取为区间端点，迭代6次或误差小于0.00001)o#include#includeintmain(){floatxl,x,fl,⑵staticintcount=0;xl=0.1;〃定义初始值do{x=xl;fl=x*(x*x*x*x*x*x-28*x*x*x)+14;f2=7*x*x*x*x*x*x-4*28*x*x*x;〃对函数fl求导xl=x-fl/f2;count++;}while(fab

2、s(xl-x)>=le-5);printf("%8.7f,,,xl);printf("%d",count);return0;}2•已知函数值如下表:X12f(x)00.69314718X67f(x)1.79175951.9459101f'(x)r(i)=i3451.09861231.38629441.609437889102.0794452.19722462.3025851r(io)=o.i试用三次样条插值求f(4.563)及fz(4.563啲近似值。inelude#inelude

3、11main(){doubleB[N+l][N+l]'rTbx,u[N+l],y[N+：l]£[N+l.],d[N+l.];doublee[N+l]={2,0,4.15888308,6.5916738,8.3177664,9.6566268,10.750557,11.6754606,12.47667,13.1833476,13.8155106,14.0155106};inti;x=4.563;B[0][0]=-2;B[0][l]=-4;B[N][N-1]=4;B[N][N]=2;for(i=l;i

4、[i][i]=4;B[i][i+l]=l;}u[O]=B[O][O];y[O]=e[O];for(i=l;i=0;i-)c[i]=(y[i]-B[i][i+l]*c[i+l])/u[i];for(i=0;i<12;i++){m=fabs(x-i);if(m>=2)d[i]=O;else讦(m<=l)d[i]=0.5*fabs(pow(m/3))-m*m+2.0/3;elsem=0;for(i=0;i<12;i++)m=m+c[i]*

5、d[i];printf(,,f(%4.3f)=%f,,,x,m);printf(,,f,(4.563)=%lf,,,(c⑷・c⑵)⑵；}3•用Romberg算法求『3*4(5兀+7)sin〒如允许误差£=0.00001).#inelude"stdafx.h"#include#includefloatf(floatx){floatf=0.0;f=pow(3.0,x)*pow(x,1.4)*(5*x+7)*sin(x*x);return(f);}main(){inti=l,j,k,n=12;T[0]=

6、0.5*(b-a)*(f(a)+f(b));for(j=l;j0・00001;i++){T[O]=T[11];for(j=l;j

7、l);T[ll]=(pow(4,i+l)*T[l]-T[0])/(pow(4,i+l)-l);}printf("%f",T[ll]);}4.用定步长四阶Runge-Kutta求解一、程序要求用定步长四阶法求解yl'=1y2'=y3y3?=1000-1000y2-100y3(yl(0)=y2(0)=y3(0)=0)h=0.0005,打印yi(0.025)/yi(0.045),yi(0.085)/yi(0.1),(i=l,2,3)dy{/dt=Idy2/dt=y.dy3/dt=1000-1000y2-100y3y.(o)=oy2(o)=o

8、y(o)=oy/(0.045),y/(0.085),yz(0.1),(/=1,2,3)#include"stdafx.h"#inelude#inelude