The document contains C++ code for numerical methods to find roots of equations including the bisection method, false position method, Newton-Raphson method, and secant method. It also contains code to calculate mean, median, and mode from grouped and ungrouped data, including arithmetic mean, geometric mean, and harmonic mean. The code shows how to convert ungrouped data to grouped data by assigning data to ranges and calculating frequencies.

1. EE 3122 Numerical
Methods and Statistics
Sessional Credit: 0.75
BY RBM GEORGE EEE_2K11
11/12/2015 RBM 1

2. Bisection Method (in Matlab)
11/12/2015 2
clc;
f=input ('Enter the co-efficient of function:');
xl=input ('Enter the value of lower limit:');
xu=input ('Enter the value of upper limit:');
fl=polyval(f,xl);
fu=polyval(f,xu);
if fl*fu>0
fprintf ('error We must have f(xl)f(xu)<0 to find a root');
break;
end
err=abs((xu-xl)/xu);
while err>.0001
xc=(xl+xu)/2;
fc=polyval(f,xc);
if fl*fc<0
xu=xc;
else
xl=xc;
end
err=abs((xu-xl)/xu);
fprintf ('xl:%f || xu:%f || Error:%f || Xc:%fn',xl,xu,err,xc);
end
RBM

3. Bisection Method (in C++)
11/12/2015 3
#include <iostream>
#include <cmath>
#include <iomanip>
using namespace std;
int main()
{
cout.setf(ios::fixed,ios::floatfield); // set fixed floating format
cout.precision(4); // for fixed format, five decimal places
float xl,xu,fl,fu,xc,fc,err;
int i;
cout<<"Enter the value of lower limit & upper limit:"<<endl;
cin>>xl>>xu;
fl=xl*xl-4*xl-10;
fu=xu*xu-4*xu-10;
if (fl*fu>0)
{
cout<<"Error We must have f(xl)f(xu)<0 to find a root"<<endl;
}
else
{
i=0;
err=abs((xu-xl)/xu);
while (err>.0001)
{
xc=(xl+xu)/2;
fc=xc*xc-4*xc-10;
i++;
cout<<"Xl:"<<xl<<"|| Xu:"<<xu<<"|| Xc:"<<xu<<"|| Error:"<<err<<"|| Iteration:"<<i<<endl;
if (fl*fc<0)
xu=xc;
else
xl=xc;
err=abs((xu-xl)/xu);
}
}
return 0;
}
RBM

4. False Position method (in C++)
11/12/2015 4
#include <iostream>
#include <cmath>
#include <iomanip>
using namespace std;
int main()
{
cout.setf(ios::fixed,ios::floatfield); // set fixed floating format
cout.precision(4); // for fixed format, five decimal places
float xl,xu,fl,fu,xc,fc,err;
int i;
cout<<"Enter the value of lower limit & upper limit:"<<endl;
cin>>xl>>xu;
fl=xl*xl-4*xl-10;
fu=xu*xu-4*xu-10;
if (fl*fu>0)
{
cout<<"Error We must have f(xl)f(xu)<0 to find a root"<<endl;
}
else
{
i=0;
err=abs((xu-xl)/xu);
while (err>.0001)
{
xc=xl-fl*(xu-xl)/(fu-fl);
fc=xc*xc-4*xc-10;
i++;
cout<<"Xl:"<<xl<<"|| Xu:"<<xu<<"|| Xc:"<<xu<<"|| Error:"<<err<<"|| Iteration:"<<i<<endl;
if (fl*fc<0)
xu=xc;
else
xl=xc;
err=abs((xu-xl)/xu);
}
}
return 0;
}
RBM

5. Newton_Raphson method (in C++)
11/12/2015 5
#include <iostream>
#include <cmath>
#include <iomanip>
using namespace std;
int main()
{
cout.setf(ios::fixed,ios::floatfield);
cout.precision(4);
float x_initial,x_iterative,fini,fiter,d_f,err;
int i;
cout<<"Enter the initial value:";
cin>>x_initial;
fini=x_initial*x_initial*x_initial-4*x_initial*x_initial+x_initial+6;
d_f=3*x_initial*x_initial-8*x_initial+1;//diff form of function
x_iterative=x_initial-fini/d_f;
i=0;
err=abs((x_iterative-x_initial)/x_iterative);
while (err>.0001)
{
i++;
cout<<"X_initial:"<<x_initial<<"|| X_iter:"<<x_iterative<<"|| Error:"<<err<<"|| Iteration:"<<i<<endl;
x_initial=x_iterative;
fini=x_initial*x_initial*x_initial-4*x_initial*x_initial+x_initial+6;
d_f=3*x_initial*x_initial-8*x_initial+1;
x_iterative=x_initial-fini/d_f;
err=abs((x_iterative-x_initial)/x_iterative);
}
return 0;
}
RBM

6. Secant method (in C++)
11/12/2015 6
#include <iostream>
#include <cmath>
#include <iomanip>
using namespace std;
int main()
{
cout.setf(ios::fixed,ios::floatfield);
cout.precision(4);
float x1,x2,f1,f2,x3,err;
int i;
cout<<"Enter two initial values:"<<endl;
cin>>x1>>x2;
f1=x1*x1-4*x1-10;
f2=x2*x2-4*x2-10;
x3=(f2*x1-f1*x2)/(f2-f1);
i=0;
err=abs((x3-x2)/x3);
while (err>.0001)
{
i++;
cout<<"X1:"<<x1<<"|| X2:"<<x2<<"|| Estimated Root:"<<x3<<"|| Error:"<<err<<"|| Iteration:"<<i<<endl;
x1=x2;
x2=x3;
f1=x1*x1-4*x1-10;
f2=x2*x2-4*x2-10;
x3=(f2*x1-f1*x2)/(f2-f1);
err=abs((x3-x2)/x3);
}
return 0;
}
RBM

7. Convert ungrouped data to grouped data (in C++)
11/12/2015 7
#include <iostream>
using namespace std;
int main()
{
int n,i,range,g,ini;
cout<<"Assign total data elements: ";
cin>>n;
float a[n];
cout<<"Enter datas one by one then press "Enter":"<<endl;
for (i=1; i<=n; i++)
{
cin>>a[i];
}
cout<<"Assign group Range: ";
cin>>range;
cout<<"Assign initial value of the group:";
cin>>ini;
g=ini;
cout<<"n"Group: "<<g<<"-"<<g+range<<"": "<<endl;
for (i=1; i<=n; i++)
{
cout <<" Data:"<<i<<" ="<<a[i]<<endl;
if(((i%range)==0)&&(i<n))
{
cout<<"nn"Group: "<<g+range<<"-"<<g+range+range<<"": "<<endl;
g=g+range;
}
}
return 0;
}
RBM

8. Calculate Mean (AM,GM,HM),mode median from ungrouped data (in C++)
11/12/2015 8
#include<iostream>
#include<cmath>
using namespace std;
int main()
{
//For UnGrouped:
int i,j,n;
cout<<"Assign total Datas' Num: ";
cin>>n;
float a[n],sum=0,mul=1,inv=0,median,t;
cout<<"Enter Datas one by one & then Press "Enter" :"<<endl;
for(i=1; i<=n; i++)
{
cin>>a[i];
sum=sum+a[i];
mul=mul*a[i];
inv=inv+(1/a[i]);
}
cout<<"For ungrouped data elements:"<<endl;
cout<<"AM:"<<(sum/n)<<" GM:"<<pow(mul,(float)1/n)<<" HM:"<<(n/inv);
////Median values:
for(i=1; i<=n; i++)
{
for (j=i+1; j<=n; j++)
{
if(a[i]>=a[j])
{
t=a[i];
a[i]=a[j];
a[j]=t;
}
}
}
if (n%2==0)
{
median=a[n/2];
}
else
{
median=a[(n+1)/2];
}
cout<<"nMedian value: "<<median;
return 0;
}
RBM

9. Calculate Mean (AM,GM,HM),mode median from grouped data(in C++)
11/12/2015 9
#include<iostream>
#include<cmath>
using namespace std;
int main()
{
//For Grouped:
int i,n;
cout<<"Assign total Datas' Num: ";
cin>>n;
float a[n],sum=0,mul=1,inv=0,f,freq[n];
cout<<"nnEnter "Data" <space> "frequency" <Enter>:"<<endl;
for(i=1; i<=n; i++)
{
cin>>a[i]>>freq[i];
f=freq[i];
sum=sum+(a[i]*f);
mul=mul*pow(a[i],(float)f);
inv=inv+(f/a[i]);
}
for(i=1; i<=n; i++)
{
cout<<"X"<<i<<"= "<<a[i]<<" & f"<<i<<"= "<<freq[i]<<endl;
}
cout<<"nnFor grouped data elements:"<<endl;
cout<<"AM:"<<(sum/n)<<"nGM:"<<pow(mul,(float)1/n)<<"nHM:"<<(n/inv);
RBM
//Median
int range,ini[n],fin[n],fc[n],m_index;
float median_class,median_value;
cout<<"nEnter group range: ";
cin>>range;
cout<<"Set initial value of Group :";
cin>>ini[1];
fc[0]=0;
for (i=1; i<=n; i++)
{
ini[i+1]=ini[i]+range;
fin[i]=ini[i+1];
fc[i]=fc[i-1]+freq[i];
cout<<"Index "<<i<<" : ";
cout<<ini[i]<<"-"<<fin[i]<<" :f= "<<freq[i]<<" fc= "<<fc[i]<<endl;
}
if (fc[n]%2==0)
{
median_class=(fc[n]/2);
}
else
{
median_class=((fc[n]+1)/2);
}
cout<<"nMedian Class:"<<median_class<<endl;
cout<<"Find out Median_Class Index in above:";
cin>>m_index;
cout<<"Lower class bowndary of median class,L1: "<<ini[m_index]<<endl;
cout<<"Total frequency,N: "<<fc[n]<<endl;
cout<<"Sum of freq lower than median class: "<<fc[m_index-1]<<endl;
cout<<"Frequency of median class,fm: "<<fc[m_index]<<endl;
cout<<"Size of the median class interval :"<<range<<endl;
median_value=(ini[m_index]+(((median_class)-fc[m_index-1])*range/fc[m_index]));
cout<<"nMedian value : "<<median_value;
return 0;
}