Program to find root of an equations using secant method

The secant method is used to find the root of an equation f(x) = 0. It is started from two distinct estimates x1 and x2 for the root. It is an iterative procedure involving linear interpolation to a root. The iteration stops if the difference between two intermediate values is less than convergence factor.

Examples :

Input : equation = x3 + x - 1 
        x1 = 0, x2 = 1, E = 0.0001
Output : Root of the given equation = 0.682326
         No. of iteration=5

Algorithm

Initialize: x1, x2, E, n         // E = convergence indicator
calculate f(x1),f(x2)

if(f(x1) * f(x2) = E); //repeat the loop until the convergence
    print 'x0' //value of the root
    print 'n' //number of iteration
}
else
    print "can not found a root in the given interval"

C++

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// C++ Program to find root of an 
// equations using secant method
#include <bits/stdc++.h>
using namespace std;
// function takes value of x and returns f(x)
float f(float x)
{
    // we are taking equation as x^3+x-1
    float f = pow(x, 3) + x - 1;
    return f;
}
  
void secant(float x1, float x2, float E)
{
    float n = 0, xm, x0, c;
    if (f(x1) * f(x2) < 0) {
        do {
            // calculate the intermediate value
            x0 = (x1 * f(x2) - x2 * f(x1)) / (f(x2) - f(x1));
  
            // check if x0 is root of equation or not
            c = f(x1) * f(x0);
  
            // update the value of interval
            x1 = x2;
            x2 = x0;
  
            // update number of iteration
            n++;
  
            // if x0 is the root of equation then break the loop
            if (c == 0)
                break;
            xm = (x1 * f(x2) - x2 * f(x1)) / (f(x2) - f(x1));
        } while (fabs(xm - x0) >= E); // repeat the loop
                                // until the convergence
  
        cout << "Root of the given equation=" << x0 << endl;
        cout << "No. of iterations = " << n << endl;
    } else
        cout << "Can not find a root in the given inteval";
}
  
// Driver code
int main()
{
    // initializing the values
    float x1 = 0, x2 = 1, E = 0.0001;
    secant(x1, x2, E);
    return 0;
}

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Java

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// Java Program to find root of an 
// equations using secant method
class GFG {
      
    // function takes value of x and 
    // returns f(x)
    static float f(float x) {
          
        // we are taking equation 
        // as x^3+x-1
        float f = (float)Math.pow(x, 3
                               + x - 1;
                                 
        return f;
    }
      
    static void secant(float x1, float x2,
                                float E) {
          
        float n = 0, xm, x0, c;
        if (f(x1) * f(x2) < 0
        {
            do {
                  
                // calculate the intermediate
                // value
                x0 = (x1 * f(x2) - x2 * f(x1))
                            / (f(x2) - f(x1));
          
                // check if x0 is root of
                // equation or not
                c = f(x1) * f(x0);
          
                // update the value of interval
                x1 = x2;
                x2 = x0;
          
                // update number of iteration
                n++;
          
                // if x0 is the root of equation 
                // then break the loop
                if (c == 0)
                    break;
                xm = (x1 * f(x2) - x2 * f(x1)) 
                            / (f(x2) - f(x1));
                              
                // repeat the loop until the 
                // convergence 
            } while (Math.abs(xm - x0) >= E); 
                                                  
            System.out.println("Root of the" +
                    " given equation=" + x0);
                      
            System.out.println("No. of "
                      + "iterations = " + n);
        
          
        else
            System.out.print("Can not find a"
              + " root in the given inteval");
    }
      
    // Driver code
    public static void main(String[] args) {
          
        // initializing the values
        float x1 = 0, x2 = 1, E = 0.0001f;
        secant(x1, x2, E);
    }
}
  
// This code is contributed by Anant Agarwal.

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Python3

# Python3 Program to find root of an
# equations using secant method

# function takes value of x
# and returns f(x)
def f(x):

# we are taking equation
# as x^3+x-1
f = pow(x, 3) + x – 1;
return f;

def secant(x1, x2, E):
n = 0; xm = 0; x0 = 0; c = 0;
if (f(x1) * f(x2) < 0): while True: # calculate the intermediate value x0 = ((x1 * f(x2) - x2 * f(x1)) / (f(x2) - f(x1))); # check if x0 is root of # equation or not c = f(x1) * f(x0); # update the value of interval x1 = x2; x2 = x0; # update number of iteration n += 1; # if x0 is the root of equation # then break the loop if (c == 0): break; xm = ((x1 * f(x2) - x2 * f(x1)) / (f(x2) - f(x1))); if(abs(xm - x0) < E): break; print("Root of the given equation =", round(x0, 6)); print("No. of iterations = ", n); else: print("Can not find a root in ", "the given inteval"); # Driver code # initializing the values x1 = 0; x2 = 1; E = 0.0001; secant(x1, x2, E); # This code is contributed by mits [tabby title="C#"]

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// C# Program to find root of an 
// equations using secant method
using System;
  
class GFG {
      
    // function takes value of 
    // x and returns f(x)
    static float f(float x) 
    {
          
        // we are taking equation 
        // as x^3+x-1
        float f = (float)Math.Pow(x, 3) 
                                + x - 1;
        return f;
    }
      
    static void secant(float x1, float x2,
                    float E)                 
                      
    {
          
        float n = 0, xm, x0, c;
        if (f(x1) * f(x2) < 0) 
        {
            do {
                  
                // calculate the intermediate
                // value
                x0 = (x1 * f(x2) - x2 * f(x1))
                    / (f(x2) - f(x1));
          
                // check if x0 is root of
                // equation or not
                c = f(x1) * f(x0);
          
                // update the value of interval
                x1 = x2;
                x2 = x0;
          
                // update number of iteration
                n++;
          
                // if x0 is the root of equation 
                // then break the loop
                if (c == 0)
                    break;
                xm = (x1 * f(x2) - x2 * f(x1)) 
                    / (f(x2) - f(x1));
                              
                // repeat the loop until 
                // the convergence 
            } while (Math.Abs(xm - x0) >= E); 
                                                  
            Console.WriteLine("Root of the" +
                    " given equation=" + x0);
                      
            Console.WriteLine("No. of "
                              "iterations = " + n);
        
          
        else
            Console.WriteLine("Can not find a"
                              " root in the given inteval");
    }
      
    // Driver code
    public static void Main(String []args) 
    {
          
        // initializing the values
        float x1 = 0, x2 = 1, E = 0.0001f;
        secant(x1, x2, E);
    }
}
  
// This code is contributed by vt_m.

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PHP

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<?php
// PHP Program to find root of an 
// equations using secant method
  
// function takes value of x 
// and returns f(x)
function f( $x)
{
      
    // we are taking equation
    // as x^3+x-1
    $f = pow($x, 3) + $x - 1;
    return $f;
}
  
function secant($x1, $x2, $E)
{
    $n = 0; $xm;
    $x0; $c;
    if (f($x1) * f($x2) < 0) 
    {
        do {
              
            // calculate the intermediate value
            $x0 = ($x1 * f($x2) - $x2
                  f($x1)) / (f($x2) - f($x1));
  
            // check if x0 is root 
            // of equation or not
            $c = f($x1) * f($x0);
  
            // update the value of interval
            $x1 = $x2;
            $x2 = $x0;
  
            // update number of iteration
            $n++;
  
            // if x0 is the root of equation
            // then break the loop
            if ($c == 0)
                break;
            $xm = ($x1 * f($x2) - $x2 * f($x1)) / 
                              (f($x2) - f($x1));
                                
        // repeat the loop
        // until the convergence
        } while (abs($xm - $x0) >= $E); 
          
        echo "Root of the given equation=". $x0."\n" ;
        echo "No. of iterations = ". $n ;
          
    } else
        echo "Can not find a root in the given inteval";
}
  
// Driver code
{
      
    // initializing the values
    $x1 = 0; $x2 = 1; 
    $E = 0.0001;
    secant($x1, $x2, $E);
    return 0;
}
  
// This code is contributed by nitin mittal.
?>

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Output :

Root of the given equation = 0.682326
No. of iterations = 5

Time Complexity = O(1)

Reference
https://en.wikipedia.org/wiki/Secant_method

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