计算方法实验汇总

#include<stdio.h>
#include<math.h>

float lmd=2;

float fa(float x)
{
    return x-lmd*(x*x*x-3*x-1)/(3*x*x-3);
}

main()
{
    float x0,x1,x2,eps;
    int count=0;
    printf("请输入迭代初值:
");
    scanf("%f",&x1);
    printf("请输入精度:
");
    scanf("%f",&eps);
    do
    {
        lmd/=2;
        x2=fa(x1);
    }while(fabs(fa(x2))>=fabs(fa(x1)));
    do
    {
        x0=x1;
        x1=fa(x0);
        count++;
    }while(fabs(x1-x0)>eps);
    printf("x*=%f
",x1);
    printf("迭代次数:%d
",count);
}

#include<stdio.h>
#include<math.h>
main()
{
    int i,j,k=1;
    double sum,max;
    double a[3][3]={{10,-1,-2},{-1,10,-2},{-1,-1,5}};
    double b[3]={7.2,8.3,4.2};
    double x[3]={0,0,0},eps;
    double y[3];
    printf("请输入精度:");
    scanf("%lf",&eps);
    while(k<100)
    {
        for(i=0;i<3;i++)
        {
            sum=0;
            for(j=0;j<3;j++)
            if(i!=j)  sum+=a[i][j]*x[j];
            y[i]=(b[i]-sum)/a[i][i];
        }
        max=0;
        printf("第%d次迭代结果: ",k);
        for(i=0;i<3;i++)
            printf("%f ",y[i]);
        printf("
");
        for(j=0;j<3;j++)
            if(max<fabs(y[j]-x[j]))  max=fabs(y[j]-x[j]);
        if(max<eps) break;
        else 
        {
            for(j=0;j<3;j++)
               x[j]=y[j];
            k++;
        }
    }
    if(k==100)  printf("error
");
}

#include<stdio.h>
#include<math.h>
main()
{
    int i,j,k=1;
    double sum,max;
    double a[3][3]={{10,-1,-2},{-1,10,-2},{-1,-1,5}};
    double b[3]={7.2,8.3,4.2};
    double x[3]={0,0,0},eps;
    double y[3]={0,0,0};
    printf("请输入精度:");
    scanf("%lf",&eps);
    while(k<100)
    {
        for(i=0;i<3;i++)
        {
            sum=0;
            for(j=0;j<3;j++)
            if(i!=j)  sum+=a[i][j]*x[j];
            x[i]=(b[i]-sum)/a[i][i];
        }
        max=0;
        printf("第%d次迭代结果: ",k);
        for(i=0;i<3;i++)
            printf("%f ",x[i]);
        printf("
");
        for(j=0;j<3;j++)
            if(max<fabs(y[j]-x[j]))  max=fabs(y[j]-x[j]);
        if(max<eps) break;
        else 
        {
            for(j=0;j<3;j++)
               y[j]=x[j];
            k++;
        }
    }
    if(k==100)  printf("error
");
}

#include<stdio.h>
const int N=5;
double x[]={0.4,0.55,0.65,0.80,0.95,1.05};
double y[]={0.41075,0.57815,0.69675,0.90,1.00,1.25382};

double Lagrange(double z)
{
    double r=0;
    int i,j;
    for(i=0;i<=N;i++)
    {
        double m=1;
        for(j=0;j<=N;j++)
        {
            if(j!=i)
                m*=(z-x[j])/(x[i]-x[j]);
        }
        r+=m*y[i];
    }
    return r;
}
main()
{
    printf("f(0.596)=%f
",Lagrange(0.596));
    printf("f(0.99)=%f
",Lagrange(0.99));
}

#include<stdio.h>
main()
{
    double a[12][12],b[11],m;
    int i,j,k;
    FILE *fp;
    fp=fopen("D:\Gauss.txt","r");
    for(i=1;i<=10;i++)
    {
        for(j=1;j<=10;j++)
            fscanf(fp,"%lf",&a[i][j]);
        fscanf(fp,"%lf",&b[i]);
    }
    fclose(fp);
    for(j=1;j<=9;j++)
    {
        for(i=j+1;i<=10;i++)
        {
            m=a[i][j]/a[j][j];
            for(k=j;k<=10;k++)
            {
                a[i][k]=a[i][k]-m*a[j][k];
            }
            b[i]=b[i]-m*b[j];
        }
    }
    for(i=10;i>0;i--)
    {
        double sum=0;
        for(j=i+1;j<=10;j++)
        {
            sum+=a[i][j]*b[j];
        }
            b[i]=(b[i]-sum)/a[i][i];
    }
    for(i=1;i<=10;i++)
        printf("x%d=%f
",i,b[i]);
}

#include<stdio.h>
#include<math.h>
main()
{
    double a[11][11],b[11],m,temp;
    int i,j,k,max;
    FILE *fp;
    fp=fopen("D:\Gauss.txt","r");
    for(i=1;i<=10;i++)
    {
        for(j=1;j<=10;j++)
            fscanf(fp,"%lf",&a[i][j]);
        fscanf(fp,"%lf",&b[i]);
    }
    fclose(fp);
    for(i=1;i<=10;i++)
    {
        max=i;
        for(j=i+1;j<=10;j++)
        {
            if(fabs(a[j][i])>fabs(a[i][i]))
                max=j;
        }
        for(j=1;j<=10;j++)
        {
            temp=a[i][j];
            a[i][j]=a[max][j];
            a[max][j]=temp;
        }
        temp=b[i];
        b[i]=b[max];
        b[max]=temp;
        for(k=i+1;k<=10;k++)
        {
            m=a[k][i]/a[i][i];
            for(j=i;j<=10;j++)
                a[k][j]=a[k][j]-m*a[i][j];
            b[k]=b[k]-m*b[i];
        }
    }
    for(i=10;i>0;i--)
    {
        double sum=0;
        for(j=i+1;j<=10;j++)
            sum+=a[i][j]*b[j];
        b[i]=(b[i]-sum)/a[i][i];
    }
    for(i=1;i<=10;i++)
        printf("x%d=%f
",i,b[i]);
}

#include<stdio.h>
#include<math.h>

#define maxn 1000
#define m 3

double x[]={0,5,10,15,20,25,30,35,40,45,50,55};
double y[]={0,0.000127,0.000216,0.000286,0.000344,0.000387,0.000415,0.000437,0.000451,0.000458,0.000402,0.000464};
double xx[maxn],bb[maxn],gauss[maxn][maxn],temp;
double b[maxn];


main()
{
    int i,j,k,max;
    double mm;
    xx[0]=12;
    for(i=1;i<=6;i++)              
    {
        xx[i]=0;
        for(k=0;k<12;k++)
        {
            temp=1;
            for(j=0;j<i;j++)
               temp*=x[k];
            xx[i]+=temp;
        }
    }

    for(i=1;i<=m+1;i++)              //系数矩阵
    {
        b[i]=0;
        for(k=0;k<12;k++)
        {
            temp=1;
            for(j=0;j<i-1;j++)
                temp*=x[k];
            b[i]+=temp*y[k];
        }
    }


    for(i=1;i<=m+1;i++)                 //建立矩阵
    {
        for(j=1;j<=m+1;j++)
            gauss[i][j]=xx[i-1+j-1];
    }


    for(i=1;i<=m+1;i++)
    {
        max=i;
        for(j=i+1;j<=m+1;j++)
        {
            if(fabs(gauss[j][i])>fabs(gauss[i][i]))
                max=j;
        }
        for(j=1;j<=m+1;j++)
        {
            temp=gauss[i][j];
            gauss[i][j]=gauss[max][j];
            gauss[max][j]=temp;
        }
        temp=b[i];
        b[i]=b[max];
        b[max]=temp;
        for(k=i+1;k<=m+1;k++)
        {
            mm=gauss[k][i]/gauss[i][i];
            for(j=i;j<=m+1;j++)
                gauss[k][j]=gauss[k][j]-mm*gauss[i][j];
            b[k]=b[k]-mm*b[i];
        }
    }
    for(i=m+1;i>0;i--)
    {
        double sum=0;
        for(j=i+1;j<=m+1;j++)
            sum+=gauss[i][j]*b[j];
        b[i]=(b[i]-sum)/gauss[i][i];
    }
    for(i=1;i<=m+1;i++)
        printf("a%d=%f
",i-1,b[i]);
}

#include<stdio.h>
#include<math.h>
#define N 250

double f(double x)
{
    return sqrt(4-sin(x)*sin(x));
}

void main()
{
    double a=0,b=1/4;
    double h=(b-a)/N,T=0;
    int k;
    for(k=1;k<N;k++)
    {
        T+=f(a+k*h);;
    }
    T=h/2*(f(a)+2*T+f(b));
    printf("%f",T);
}

#include<stdio.h>
#include<math.h>
#define N 4000

double f(double x)
{
    if(x==0)  return 1;
    else return sin(x)/x;
}

void main()
{
    double a=0,b=1;
    double h=(b-a)/N;
    double s1=f(a+h/2),s2=0;
    int k;
    for(k=0;k<N;k++)
    {
        s1+=f(a+k*h+h/2);
        s2+=f(a+k*h);
    }
    s1=h/6*(f(a)+4*s1+2*s2+f(b));
    printf("%f",s1);
}

#include<stdio.h>
#include<math.h>

double f(double x)
{
    if(x==0)  return 1;
    else return sin(x)/x;
}

void main()
{
    int i,n=1,k=0;
    double a=0,b=1,sum;
    double T1,T2,h,S1,S2=0,C1,C2=0,R1,R2=0,eps=0.00001;
    h=(b-a)/2;
    T2=h*(f(a)+f(b));    
    while(fabs(R2-R1)>eps)
    {
        R1=R2;
        T1=T2;
        S1=S2;
        C1=C2;
        sum=0;
        for(i=1;i<=n;i++)
        {
            sum=sum+f(a+(2*i-1)*h);
        }
        T2=T1/2+sum*h;
        S2=(4*T2-T1)/3;
        C2=(16*S2-S1)/15;
        R2=(64*C2-C1)/63;
        n=n*2;
        k++;
        h=h/2;
    }
    printf("%f",R2);
}

#include<stdio.h>
#include<math.h>
#define N 5


double f(double x,double y)
{
    return y-2*x/y;
}


main()
{
    double x0=0,x1,y0=1,y1,h=0.2;
    double k1,k2,k3,k4;
    int n=1,i=1;
    do
    {
        x1=x0+h;
        k1=f(x0,y0);
        k2=f(x0+h/2,y0+h/2*k1);
        k3=f(x0+h/2,y0+h/2*k2);
        k4=f(x1,y0+h*k3);
        y1=y0+h/6*(k1+2*k2+2*k3+k4);
        printf("n=%d,x%d=%f,y%d=%f
",n,i,x1,i,y1);
        i++;
        n++;
        x0=x1;
        y0=y1;
    }while(n<N+1);
}