C program for secant methodThe Secant Method stands out as an effective and potent numerical method for solving quadratic equations. The Secant Method is renowned for its precision and ease of use, and it is especially effective at locating the roots of quadratic equations. In this article, the principles of the Secant Method will be examined, along with its application in C programming and a practical example complete with code and results. The Secant Method is a type of iterative numerical method for approximating an equation's roots. The Secant Method avoids the need for derivatives, in contrast to Newton's Method and other approaches, earning it the nickname "Newton's Method without Division". The main concept behind the method is to convert a quadratic equation into two linear equations, which are then used to calculate the root values. Ways to Implement the Secant Method:The Secant Method in C programming can be implemented in the following ways:
Example:Output: Enter the values of a and b: 1 2 Enter the values of allowed error and maximum number of iterations: 0.0001 10 Iteration No-1 x=2.333333 Iteration No-2 x=1.897810 Iteration No-3 x=1.751373 Iteration No-4 x=1.730823 Iteration No-5 x=1.732114 The required solution is 1.732114 Explanation: In this C program, the Secant Method is used to roughly get the root of the equation x3 - 4 = 0. Initial guesses 'a' and 'b' are entered by users, along with the number of iterations 'n' and the permitted error 'e'. To get closer to the root, it changes 'a' and 'b' iteratively, outputting the most recent approximation after each update. When the fault occurs within 'e' iterations or 'n' iterations, the program terminates. Conclusion:In conclusion, the Secant Method demonstrated to be an effective method for approximating the roots of quadratic equations with high precision. It is effective and trustworthy because of its distinctive method of converting quadratic problems into linear ones combined with iterative refining. This article discussed the fundamentals of the Secant Method, how it may be applied to C programming, and presented a useful code example. By mastering the Secant Method, programmers expand their arsenal for numerical analysis and get a flexible method for solving challenging mathematical problems. The given example shows how effective it is in practice and demonstrates how quickly it can converge to precise root estimations.
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