Secant Method C++ Program, Formula, Example

What is Secant Method

Intro:

The Secant Method is used to find the roots of an equation.

The Secant method is similar to the Regula-Falsi method, except for the fact that we drop the condition that f(x) should have opposite signs at the two points used to generate the next approximation.

Instead, we always retain the last two points to generate the next. Thus, if x_i-1 and x_i are two approximations to the root, then the next approximation x_i+1 to root is given by the following equation.

Secant Method Formula

In contrast to the Regula-Falsi method, the Secant method does not bracket the root and it is not even necessary to bracket the root to start the iteration.

Hence, it is obvious that the iteration may not always coverage. On the other hand, it generally converges faster.

Algorithm for Secant Method

Step 1: Choose i=1

Step 2: Start with the initial guesses, x_i-1 and x_i

Step 3: Use the formula

Step 4: Find Absolute Error,|Ea|= |(X_i+1 -Xi)/X_i+1|*100

            Check if |Ea| <= Es (Prescribed tolerance)

            If true then stop

            Else go to step 2 with estimate X_i+1, X_i

Secant Method C++ Program

Secant Method C++ Program for function f(x) = x²-2x-5

  //Program: Secant Method using C++
     //techindetail.com

#include<iostream>
#include<cmath>

 //for specifying format
#include<bits/stdc++.h>	

using namespace std;

  //prespecified error tolerance
#define Es 0.0001

float F(float x){
	float res;
	res=(x*x)-(2*x)-5;
	return res;
} 

int main(){
	float x0,x1,x2,x2old,f0,f1,f2;
	int itr=1;
	float Ea;
	cout<<"Enter the intial guesses (x0,x1): ";
	cin>>x0>>x1;
	cout<<"Itr No.\tx0\tx1\tf0\tf1\tx2\t f2\tEa\n";
	cout<<"----------------------------------------------------------------------------\n";
	while (1){
		f0=F(x0);
		f1=F(x1);		
		x2=x1-(f1*(x1-x0)/(f1-f0));
		f2=F(x2);
		
		//finding absolute error
		Ea=fabs((x2-x1)/x2);
		cout<<fixed<<setprecision(3);
	cout<<itr<<"\t"<<x0<<"\t"<<x1<<"\t"<<f0<<"\t"<<f1<<"\t"<<x2<<"\t"<<f2<<"\t"<<Ea<<"\n";	
		x0=x1;
		x1=x2;
		itr++;
		if(Ea<=Es)
			break;	
	}
	cout<<"Approximate root (x2) is: "<<x2;
	return 0;
} 
Code language: C++ (cpp)

Output:

Secant Method Example

Related Numerical Methods: