A Generalized Regula Falsi Method for Finding Zeros and Extrema of Real Functions. (30th July 2013)

• Record Type: Journal Article
• Authors: Gomes, Abel; Morgado, José
• Other Names: Nguyen-Xuan Hung Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2013(2013)
• Publication Date: 2013-07-30
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2013/394654
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : Many zero-finding numerical methods are based on the Intermediate Value Theorem, which states that a zero of a real function f : ℝ → ℝ is bracketed in a given interval A, B ⊂ ℝ if f A and f B have opposite signs; that is, f A · f B < 0 . But, some zeros cannot be bracketed this way because they do not satisfy the precondition f A · f B < 0 . For example, local minima and maxima that annihilate f may not be bracketed by the Intermediate Value Theorem. In this case, we can always use a numerical method for bracketing extrema, checking then whether it is a zero of f or not. Instead, this paper introduces a single numerical method, called generalized regula falsi (GRF) method to determine both zeros and extrema of a function. Consequently, it differs from the standard regula falsi method in that it is capable of finding any function zero in a given interval A, B ⊂ ℝ even when the Intermediate Value Theorem is not satisfied.