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Код

double f_root(double y);//y-na4alnoe priblijenie
double g_root(double x);
double norm (double x0, double x1, double y0, double y1);
double f(double x, double y);
double g(double x, double y);

int _tmain(int argc, _TCHAR* argv[])
{
    double x, xnext, y, ynext;
    int t=1;
    int n=0, m=0;
    x=0.5; y=0.5;  // начальное приближение
    while (t!=0)
    {
        xnext=f_root( y);
        //cout<<xnext<<endl;
        ynext=g_root(x);
        //cout<<ynext<<endl;
        n++;
        if (norm(x, xnext, y, ynext)<0.0001) t=0;
        //if (n==65000){ n=0; m++;}
        if (n==65000) t=0;
        x=xnext;
        y=ynext;
    }
    cout<<"x="<<x<<"\ty="<<y<<"\nn="<<n<<"\nm="<<m<<endl;;
    system("pause");
    return 0;
}

double f_root( double y)//y-na4alnoe priblijenie
{
    double x0=0,x1=2,res;
l1:    if (f(x0, y)*f(x1, y)>=0)
    {
        x1++;
        x0--;
        goto l1;
    }
    else
    {        
        while (true) 
        {    
            res=(x1+x0)/2;
            if (f(x0, y)>0)
            {
                if (f(res, y)>0) x0=res; else x1=res;
            }
            else //if (function1(x0)<0)
            {
                if(f(res, y)<0) x0=res; else x1=res;
            }
            //cout<<x0<<" "<<x1<<endl;
            if (abs(x1-x0)<0.00001) break;
        };
    }
    return (x1+x0)/2;
}
double g_root(double x)
{
    double x0=0,x1=2,res;
l2:    if (g(x, x0)*g(x, x1)>=0)
    {
        x1++;
        //x0--;
        goto  l2;
    }
    else
    {        
        while (true) 
        {    
            res=(x1+x0)/2;
            if (g(x, x0)>0)
            {
                if (g(x, res)>0) x0=res; else x1=res;
            }
            else //if (function1(x0)<0)
            {
                if(g(x, res)<0) x0=res; else x1=res;
            }
            //cout<<x0<<" "<<x1<<endl;
            if (abs(x1-x0)<0.00001) break;
        }
    }
    return (x1+x0)/2;
}
double norm (double x0, double x1, double y0, double y1)
{
    return /*abs(x0-y0)+abs(x1-y1);//*/sqrt( (x0-x1)*(x0-x1)+(y0-y1)*(y0-y1) );
}
double f(double x, double y)
{
    return x*x+y*y-1;
}
double g(double x, double y)
{
    return x-y;
}