Lipschitz condition for finding real roots of a vector function

Article type: Research Article

Authors: Alolyan, Ibraheem^{; *}

Affiliations: Mathematics Department, College of Science, King Saud University, Riyadh, Saudi Arabia

Correspondence: [*] Corresponding author: Mathematics Department, College of Science, King Saud University P.O.Box: 2455, Riyadh 11451, Saudi Arabia. E-mail: [email protected].

Abstract: Computing real roots of a continuous function is an old and extensively researched problem in numerical computation. Exclusion algorithms have been used recently to find all solutions of a system of nonlinear equations or to find the global minimum of a function over a compact domain. These algorithms are based on a root condition that can be applied to each cell in the domain. In the present paper, we consider Lipschitz functions of order α and give the root condition for the exclusion algorithms. Furthermore, we investigate convergence and computational complexity for such algorithms and illustrate their performance by a numerical example.

Keywords: numerical solution of nonlinear system of equation, exclusion test, Lipschitz function of order α, computational complexity

DOI: 10.3233/JCM-2011-0393

Journal: Journal of Computational Methods in Sciences and Engineering, vol. 11, no. 5-6, pp. 259-267, 2011