#include<iostream.h>
#include<math.h>
#define LB -1
#define UB 1
using namespace std;
class Newton
{
double a,b,x0,x1,tolerance;
double Fa,Fb,Fx0,h,root[100],dFx0,Fx1,cv,pv,Fcv;
int rootIndex;
public:
Newton()
{
tolerance = 10E-4;
rootIndex = -1;
}
double fun_value(int,double);
void find_root(int);
bool validInterval(double);
double deriv_fun(int,double);
};
bool Newton::validInterval(double z)
{
if(z<0)
return true;
else
return false;
}
void Newton::find_root(int degree)
{
int count = 1;
char ch;
double diff;
h = (UB-LB)/(double)degree;
while(rootIndex < degree)
{
if(rootIndex != -1)
h = h /2;
rootIndex = 0;
for(int i = 0;i<degree;i++)
{
a = LB + (i*h);
b = LB + ((i+1)*h);
while(1)
{
Fa = fun_value(degree,a);
Fb = fun_value(degree,b);
if(validInterval(Fa*Fb))
{
x0 = (a+b)/2;
pv=x0;
while(1)
{
cv = pv - (fun_value(degree,pv)/deriv_fun(degree,pv));
Fcv = fun_value(degree,cv);
if(fabs(Fcv)<tolerance)
{
root[rootIndex++] = cv;
goto end;
}
pv = cv;
}
}
else
{
root[rootIndex++] = a;
break;
}
}//end of While
end:
cout<<"";
}//end of For
}//end of for
cout<<"\n\nThe roots are===>\n";
for(int i = 0;i<rootIndex;i++)
cout<<" "<<i+1<<". "<<root[i]<<endl;
}
double Newton::fun_value(int degree ,double x)
{
switch(degree)
{
case 0:
return 1;
case 1:
return x;
case 2:
return(2*x*x - 1);
case 3:
return (4*x*x*x - 3*x);
case 4:
return(8*x*x*x*x - 8*x*x + 1);
case 5:
return(16*x*x*x*x*x - 20*x*x*x + 5*x);
}
}
double Newton::deriv_fun(int degree ,double x)
{
switch(degree)
{
case 0:
return 0;
case 1:
return 1;
case 2:
return(4*x);
case 3:
return (12*x*x - 3);
case 4:
return(32*x*x*x - 16*x);
case 5:
return(80*x*x*x*x - 60*x*x + 5);
}
}
main()
{
Newton N;
int degree;
double *root;
cout<<"Enter the degree of equation it should be in between 0 to 5\n";
cin>>degree;
N.find_root(degree);//calculates the root
return 0;
}
Comment