Comparative Study of Complexity of Algorithms for Iterative Solution of Non-Linear Equations

Abstract

In this paper algorithms for Bisection, Secant, Rugla-Falsi, Newton Raphson and Adaptive Bisection methods to find the roots of
non-linear equation are studied for their complexity. Using RAM (Random Access Machine) model the complexity of all algorithms are
calculated. In RAM model we count the primitive operations executed by given algorithm and then find the time in function t(n). The complexity can represent in the form of Big-Oh notation in term of time function. In order to compare the adaptive Bisection method with Bisection method, Secant method, Regula-Falsi method and Newton Raphson method a variety of functions are used with same criteria i.e. 10-6. The time complexity of all algorithms are O(n) where n is number of iteration. The result shown in table shows that for function f(x) =ex-3x the number of iteration in Bisection methods are 20 while in adaptive Bisection method is 5. Since time complexity of both algorithms are O(n) , so Adaptive bisection algorithm will execute faster to compare all other method and it will take less time to run the program.