用C语言编写数值分析作业题

用C语言编写数值分析作业题：（包括高斯消元法，二分法，迭代法，牛顿迭代法）
1.二分法
#include "stdio.h"
#include "conio.h"
#include
#include

#define f(x) (x*x*x-3*x+1)

void main()
{
float eve,a,b,E=0.0001;

float function(float x);
printf("please put a:");
scanf("%f",&a);

printf("please put b:");
scanf("%f",&b);

if(f(a)*f(b)>=0)
printf("no answer");
eve=(a+b)/2;

while(fabs(f(eve))>E)
{
printf("a=%f\t",a);
printf("b=%f\t",b);
eve=(a+b)/2;
printf("eve=%f\t",eve);
printf("f(eve)=%f\n",f(eve));

if(f(eve)==0)break;
if(f(a)*f(eve)<0)
b=eve;
else
a=eve;
}

printf("the answer is:\n");
printf("%f\t",eve);
return;
}

2.高斯消元法
#include "stdio.h"
#include "conio.h"
#include

void main()
{ /* 定义各量 */
int n;
int i,j,k,t,d,xpt=0;
float sum,max,p,q,h;
float a[100][100],b[100],x[100],xp[100],l[100][100];

printf("please put n:\n");
scanf("%d",&n);

printf("please put a:");
for(i=1;i<=n;i++)
for(j=1;j<=n;j++)
scanf("%f",&a[i][j]);

printf("please put b:");
for(i=1;i<=n;i++)
scanf("%f",&b[i]);

for(k=1;k<=n-1;k++)
{
for(i=k+1;i<=n;i++)
{ if(a[k][k]!=0) l[i][k]=a[i][k]/a[k][k];
else printf("no answer\n");
a[i][k]=0;
for(j=k+1;j<=n;j++)
{a[i][j]=a[i][j]-l[i][k]*a[k][j];
}
b[i]=b[i]-l[i][k]*b[k];
}
}

if(a[n][n]==0){printf("no answer\n");}
else
{
x[n]=b[n]/a[n][n];

for(i=n-1;i>=1;i--)
{
sum=0;
for(j=i+1;j<=n;j++)
sum=sum+a[i][j]*x[j];

x[i]=(b[i]-sum)/a[i][i];
}
}

printf("the answer is:\n");
for(i=1;i<=n;i++)
printf("%f\t",x[i]);

return;
}

3.迭代法
#include
#include
#include "conio.h"
#include

double func(double x) /*函数*/
{return pow(x,3)+4*x*x-10;}

double func1(double x) /*g1(x)*/
{return x-pow(x,3)-4*x*x+10;}

double func2(double x) /*g2(x)*/
{ if((10/x-4*x)<0){ printf("no sence\n");return 1000;}
return sqrt(10/x-4*x);}

double func3(double x) /*g3(x)*/
{if((10-pow(x,3))<0){ printf("no sence\n");return 1000;}
return sqrt(10-pow(x,3))/2;
}

double func4(double x) /*g4(x)*/
{ if((10/(4+x))<0){ printf("no sence\n");return 1000;}
return sqrt(10/(4+x));}
double func5(double x) /*g5(x)*/
{return x-((pow(x,3)+4*x*x-10)/(3*x*x+8*x));}

void main()
{
int i;
double x[30],p;

/*
p=1.5;
printf("g1(x):\n");
for(i=0;i<=25;i++)
{
x[i]=p;
printf("%f\n",x[i]);
p=func1(x[i]);
if(p>5||p<-2)
{printf("no convergence or wrong\n");break; }
}

printf("\n\n");
p=1.5;
printf("g2(x):\n");
for(i=0;i<=25;i++)
{
x[i]=p;
printf("%f\n",x[i]);
p=func2(x[i]);
if(p>5||p<-2||p==0)
{printf("no convergence or wrong\n");break; }
}

printf("\n\n");
p=1.5;
printf("g3(x):\n");
for(i=0;i<=25;i++)
{
x[i]=p;
printf("%f\n",x[i]);
p=func3(x[i]);
if(p>5||p<-2)
{printf("no convergence or wrong\n");break; }
}

printf("\n\n");
p=1.5;
printf("g4(x):\n");
for(i=0;i<=10;i++)
{
x[i]=p;
printf("%f\n",x[i]);
p=func4(x[i]);
if(p>5||p<-2)
{printf("no convergence or wrong\n");break; }
}

printf("\n\n");
*/
p=1.5;
printf("g5(x):\n");
for(i=0;i<=10;i++)
{
x[i]=p;
printf("%f\n",x[i]);
p=func5(x[i]);
if(p>5||p<-2)
{printf("no convergence or wrong\n");break; }
}

getch();
}

4.牛顿迭代法
#include
#include

double func(double x)
{return pow(x,5)-4*x-2 ; }

double func1(double x)
{return 5*pow(x,4)-4 ; }

double root(double num)
{ double x0,x1;
int k=1;
x0=num;
if(func1(x0)==0.0)
{printf("迭代过程中导数为0!\n");return x0;}

printf("k=%d\t",k); k++;
printf("xk=%lf\n",x0);

x1=x0-func(x0)/func1(x0);
do
{
printf("k=%d\t",k);
printf("xk=%lf\n",x1);
k++;
x0=x1;
x1=x0-func(x0)/func1(x0);

} while((fabs(x1-x0))>1e-6);
printf("the root near 1.5 is:%lf\n",x1);
return x1;
}

void main()
{
root( 2 ) ;
}