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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.
Department of Electrical and Computer Engineering University of Waterloo 200 University Avenue West Waterloo, Ontario, Canada N2L 3G1 +1 519 888 4567. To do this, we could create an m-file for the other function, but we would have to call that m-file cosmx.m even if there were no cosines in it, because that is what the bisectcosmx function expects. Suppose that we have three files, called f1.m through f3.m, each of which evaluates a function that we want to use bisection.
The equation used in the following secant method c programs are as follows:
- x3 – 5x + 3
- x3 – 3x – 8
Secant Method Formula
Secant Method Algorithm
2 4 6 8 | Step1:Assume an equationf(x)=0(which must be defined) Step3:Do wherei=1,2,3,4,..... Step4:Evaluated Result |
Convergence criteria for Secant Method
- Fixing apriori the total number of iterations (limit).
- 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
Secant Method Excel
- 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
2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 | { floatstart_interval,end_interval,midpoint,allowed_error; printf('nEnter Value for Start Interval Point:t'); printf('nEnter Value for End Interval Point:t'); printf('nEnter Value for Allowed Error:t'); printf('nEnter Limit for Iterations:t'); do if(equation(start_interval)equation(end_interval)) printf('Please enter different start and end intervalsn'); } midpoint=(start_interval *equation(end_interval)-end_interval *equation(start_interval))/(equation(end_interval)-equation(start_interval)); end_interval=midpoint; printf('nIteration: %dtRoot: %fn',count,midpoint); if(countlimit) break; }while(fabs(equation(midpoint))>allowed_error); return0; { } |
Output
Method 2: Implement Secant Method in C Programming using While Loop
Secant Method M File Viewer
2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 | #include #define EQUATION(x) (x)*(x)*(x) - 3*(x) - 8 intmain() floatinterval_start,interval_end,midpoint; printf('nEnter Value for Start Interval Point:t'); printf('nEnter Value for End Interval Point:t'); printf('nEnter value for Allowed Error:t'); printf('n'); printf('nStartttEndttMidPointtfunction(Start)tfunction(End)'); while(temp>allowed_error) a=EQUATION(interval_start); midpoint=interval_end-((b *(interval_end-interval_start))/(b-a)); printf('n%ft%ft%ft%ft%f',interval_start,interval_end,midpoint,a,b); interval_end=midpoint; { } { } printf('nnRoot of the Equation: %fn',midpoint); |
Output
Matlab Secant Method M File
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.
| NUMERICAL METHODS C PROGRAMS |
|---|
| Newton-Raphson Method C Program |
| Weddle's Rule Algorithm C Program |
| Euler's Method C Program |
| Bisection Method C Program |
| Gauss Seidel Method C Program |
| Simpson's 3/8th Rule C Program |
| Picard's Method C Program |
| Regula Falsi Method C Program |
| Bisection Method Algorithm and Flowchart |
| Simpson's 1/3rd Rule C Program |
| Trapezoidal Rule C Program |
