Affiliation:
1. Institute of Science, Engineering and Technology, Federal University of the Valleys of Jequitinhonha and Mucuri, Brazil
2. Department of Mathematics, Federal University of Minas Gerais, Brazil
Abstract
We identify a class of root-searching methods that surprisingly outperform the bisection method on the average performance while retaining minmax optimality. The improvement on the average applies for any continuous distributional hypothesis. We also pinpoint one specific method within the class and show that under mild initial conditions it can attain an order of convergence of up to 1.618, i.e., the same as the secant method. Hence, we attain both an improved average performance and an improved order of convergence with no cost on the minmax optimality of the bisection method. Numerical experiments show that, on regular functions, the proposed method requires a number of function evaluations similar to current state-of-the-art methods, about 24% to 37% of the evaluations required by the bisection procedure. In problems with non-regular functions, the proposed method performs significantly better than the state-of-the-art, requiring on average 82% of the total evaluations required for the bisection method, while the other methods were outperformed by bisection. In the worst case, while current state-of-the-art commercial solvers required two to three times the number of function evaluations of bisection, our proposed method remained within the minmax bounds of the bisection method.
Publisher
Association for Computing Machinery (ACM)
Subject
Applied Mathematics,Software
Reference35 articles.
1. On the Secant method
2. An algorithm with guaranteed convergence for finding a zero of a function
3. Two Efficient Algorithms with Guaranteed Convergence for Finding a Zero of a Function
4. S. C. Chapra and R. P. Canale. 2010. Numerical Methods for Engineers (6th ed.). McGraw-Hill Higher Education New York NY 202--220. S. C. Chapra and R. P. Canale. 2010. Numerical Methods for Engineers (6th ed.). McGraw-Hill Higher Education New York NY 202--220.
5. A modified regula falsi method for computing the root of an equation;Dowell M.;ACM Trans. Math. Softw.,1971
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