¹Faculty of Mathematics & Computer Science, Quanzhou Normal University, China
²Faculty of Mathematics & Computer Science, Fuzhou University, China

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Abstract—Optimization has been a basic tool in all areas of applied mathematics, engineering, medicine, economics and other sciences. There has been much attention to develop iterative methods for solving nonlinear equations in these years. New algorithms and theoretical techniques have been developed, the diffusion into other disciplines has proceeded at a rapid pace. One of the most striking trends in optimization is the constantly increasing emphasis on the interdisciplinary nature of the field. Among wide various of papers have been published in the recent years, there are some progress about multi-step methods. These multi-step methods have been suggested by combining the well-known Newton’s method with other methods. In this work, we develop a simple yet practical algorithm for solving nonlinear optimization problems by solving nonlinear equations with a good local convergence. The algorithm uses a continued fraction interpolation that can be easily implemented in software packages for achieving desired convergence orders. For the general n-point formula,the order of convergence rate of the presented algorithm is T_n, the unique positive root of the equation xⁿ-xⁿ-1...-x-1 = 0. Computational results ascertain that the developed algorithm is efficient and demonstrate equal or better performance as compared with other well known methods.

Index Terms—optimization, algorithms, nonlinear equations, convergence rate, continued fraction

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Cite: Daxin Zhu, Xiaodong Wang, "An Efficient Continued Fraction Algorithm for Nonlinear Optimization and Its Computer Implementation," Journal of Computers vol. 9, no. 4, pp. 883-890, 2014.