Newton Raphson is good general purpose root finding method, but sometimes if function is very complicated then computing derivates will take much computational time, so to overcome this issue, in secant method we approximate the first order derivative term f’(r). Secant Method is also root finding method of non-linear equation in numerical method. This is an open method, therefore, it does not guaranteed for the convergence of the root. This method is also faster than bisection method and slower than Newton Raphson method. Like Regula Falsi method, Secant method is also require two initial guesses.
Secant Method/ Numerical Method /C Programming /Secant Method in C Programming / csit/ Computer science /Engineering. Secant Method method now requires two initial guesses, but unlike the bisection method, the two initial guesses do not need to bracket the root of the equation. The secant method is an open method and may or may not converge. Working of Muller Method −. Let us assume three distinct initial roots x0, x1 and x2. Now draw a parabola, through the values of function f (x) for the points- x0, x1 and x2. The equation of the parabola, p (x), will be−. P (x )=c+b ( x – x 2)+a ( x – x2)2; where a, b and c are the constants. Now, find the intersection of the parabola. Newton Raphson method in c. In numerical analysis, Newton's method (also known as the Newton–Raphson method), named after Isaac Newton and Joseph Raphson, is a method for finding successively better approximations to the roots (or zeroes) of a real-valued function.
Secant Method is also root finding method of non-linear equation in numerical method. This is an open method, therefore, it does not guaranteed for the convergence of the root. This method is also faster than bisection method and slower than Newton Raphson method. Like Regula Falsi method, Secant method is also require two initial guesses to start the solution and there is no need to find the derivative of the function. But only difference between the secant method and Regula Falsi method is that:
C Program For Secant Method With Output
- Secant method is open and Regula Falsi method is closed.
- Secant method does not guaranteed to the convergence of the root while Regula Falsi method does.
- Regula Falsi method is bracketing method but Secant method is not.
- In method of False position, check the sign of the function at each iteration but in secant method is not.
The formula of Secant method is same as False position such that:
At here, we write the code of Secant Method in MATLAB step by step. MATLAB is easy way to solve complicated problems that are not solve by hand or impossible to solve at page. MATLAB is develop for mathematics, therefore MATLAB is the abbreviation of MATrix LABoratory.
At here, we find the root of the function f(x) = x2-2 = 0 by using Secant Method with the help of MATLAB.
MATLAB Code of Secant Method
Other Numerical Methods with MATLAB Coding
Hello everyone, in this tutorial, we are going to learn how to implement the secant method in Python to find the roots of a given equation of the form f(x) = 0.
Here’s the algorithm to implement the secant method.
First, we initialize two variables x1 and x2 that are the estimated values for the root. We also initialize a variable e to define the desired accuracy and a variable for iteration(Let’s say i) in a loop. Then, for every iteration, we calculate f(x1) and f(x2) and intermediate values as shown in the code. If the difference between two intermediate values is less than the desired accuracy, we break the loop and print the result as shown.
The above has been implemented in Python below. Have a look at the given program.
C Program For Secant Method With Output Data
Output:
Explanation: In the above example, we have defined f(x) as x^4 + 2x – 1. The secant method takes three parameters x1, x2, and e. x1 and x2 are initial approximation values. These values are updated in every iteration of the loop until the difference between calculated intermediate values is less than e. The function returns the root between the given interval (initial values of x1 and x2) if a root is found with the desired accuracy. If not, then the function returns -1.
Thank you.
C Program For Secant Method With Output Example
Also read: Find the root of an equation using Newton Raphson method in C++