STUDYING THE EFFICIENCY OF ROOT FINDING METHODS

Abstract

Root finding is one of the most significant problems not only of applied mathematics, but also of engineering sciences, physics, finance etc. The implementation of efficient numerical methods to buildin functions in different software programs is a task we want to achieve. We possess different groups of methods with sufficiently good convergence order, but as we know the higher the speed is a larger amount of function and derivative evaluations per iteration is needed. The main goal in this paper is the construction of new methods with higher computational efficiency. The comparison will be made by defining the computational efficiency based on the speed of convergence, cost of evaluating the function and its derivatives and the cost of constructing the iterative process. The calculations are made using the symbolic programming language of MATLAB environment.