Accelerated Multipoint Root Finding Iterative Methods
Eglantina Kalluci1, Fatmir Hoxha2
1Dr. Eglantina Kalluci, Department of Applied Mathematics, Faculty of Natural Sciences, University of Tirana, Tirana, Albania.
2Prof. Fatmir Hoxha, Department of Applied Mathematics, Faculty of Natural Sciences, University of Tirana, Tirana, Albania.
Manuscript received on January 02, 2015. | Revised Manuscript received on January 08, 2015. | Manuscript published on January 15, 2015. | PP: 37-40 | Volume-3 Issue-2, January 2015. | Retrieval Number: B0779013215/2014©BEIESP
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© The Authors. Published By: Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
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 build-in 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. In this paper we will present new multipoint methods with higher computational efficiency, than known ones. The comparison will be made by defining the computational efficiency based on the convergence order, and the efficiency index, which measures the cost of performing iteration.
Keywords: Efficiency index, iterative method, order of convergence, root finding.