Secant method is considered to be the most effective approach to find the root of a non-linear function. It is a generalized from the Newton-Raphson method and does not require obtaining the derivatives of the function. So, this method is generally used as an alternative to Newton Raphson method.
Secant method falls under open bracket type. The programming effort may be a tedious to some extent, but the secant method algorithm and flowchart is easy to understand and use for coding in any high level programming language.
TUTORIAL 7 SJEM2231: STRUCTURED PROGRAMMING (C) //Output: SECANT METHOD sin(x)+3cos(x)-2 0.000000 1.500000 0.837851 1.500000 0.837851 1.160351 0.837851 1.160351 1.218120 1.160351 1.218120 1.207622 1.218120 1.207622 1.207827 1.207622 1.207827 1.207828 The root is 1.20783 QUESTION 6 Use Secant method to find the real root of the equation x3- 8x. 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 C Program Secant Method MATLAB Program. Secant method is an improvement over the Regula-Falsi method, as successive approximations are done using a secant line passing through the points during each iteration. Following the secant method algorithm and flowchart given above, it is not compulsory that the approximated interval. In the above code snippet, Fd denotes the Derivative of the Function F. Same approach for solving the quation F(x) = 0. This method is almost identical with Newton's Method except the fact that we choose two initial approximations instead ofone before we start the Iteration Process. 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.
This method uses two initial guesses and finds the root of a function through interpolation approach. Here, at each successive iteration, two of the most recent guesses are used. That means, two most recent fresh values are used to find out the next approximation.
Features of Secant Method:
- No. of initial guesses – 2
- Type – open bracket
- Rate of convergence – faster
- Convergence – super linear
- Accuracy – good
- Approach – interpolation
- Programming effort – tedious
Secant Method Algorithm:
- Start
- Get values of x0, x1 and e
*Here x0 and x1 are the two initial guesses
e is the stopping criteria, absolute error or the desired degree of accuracy* - Compute f(x0) and f(x1)
- Compute x2 = [x0*f(x1) – x1*f(x0)] / [f(x1) – f(x0)]
- Test for accuracy of x2
If [ (x2 – x1)/x2 ] > e, *Here [ ] is used as modulus sign*
then assign x0 = x1 and x1 = x2
goto step 4
Else,
goto step 6 - Display the required root as x2.
- Stop
Secant Method Flowchart:
C Program For Secant Method With Output Example
Also see,
Secant Method C Program
Secant Method MATLAB Program
Secant method is an improvement over the Regula-Falsi method, as successive approximations are done using a secant line passing through the points during each iteration. Following the secant method algorithm and flowchart given above, it is not compulsory that the approximated interval should contain the root.
C Program For Secant Method With Output Number
Secant method is faster than other numerical methods, except the Newton Raphson method. Its rate of convergence is 1.62, which is quite fast and high. However, convergence is not always guaranteed in this method. But, overall, this method proves to be the most economical one to find the root of a function.