Secant Method C Program

By | June 28, 2017
 

Let’s understand the secant method in numerical analysis and learn how to implement secant method in C programming with an explanation, output, advantages, disadvantages and much more.

What is Secant Method?

The secant method is a root-finding method that uses a succession of the roots of secant lines to find a better approximation of root.

The secant method algorithm is a root bracketing method and is the most efficient method of finding the root of a function. It requires two initial guesses which are the start and end interval points. This method is very similar to the Regula Falsi method.

The secant method is a Quasi-Newton method and it is seen to be faster in execution in some scenarios as compared to Newton-Raphson method and the False Position Method well.

The secant algorithm does not ensure convergence. The rate of convergence of secant method algorithm is 1.618, which is really fast comparatively. The order of convergence of secant method is superlinear.

The equation used in the following secant method c programs are as follows:

  • x3 – 5x + 3
  • x3 – 3x – 8

Secant Method Formula

Secant Method Formula For Numerical Analysis

Secant Method Algorithm

Convergence criteria for Secant Method

  1. Fixing apriori the total number of iterations (limit).
  2. Testing the condition (xi+1−xi), is less than some tolerance limit (epsilon).

Advantages

  • It evaluates one function at every iteration as compared with Newton’s method which evaluates two.
  • The convergence rate is very fast.
  • The secant method rule does not use the derivatives of a function.

Disadvantages

  • The convergence may not always happen.
  • Newton’s method generalizes much efficiently to new methods for solving simultaneous systems of nonlinear equations as compared to the Secant method.

Note: This secant method in C programming is compiled with GNU GCC compiler using CodeLite IDE on Microsoft Windows 10 operating system.

Method 1: C Program For Secant Method using Do While Loop

   

Output

Implement Secant Method in C Programming using While Loop

Method 2: Implement Secant Method in C Programming using While Loop

   

Output

C Program For Secant Method To Find Roots of Equation

If you have any doubts about the implementation of Secant method in C programming, let us know about it in the comment section. Find more about it on WikiPedia.

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