“Potential interval of root” of nonlinear equation: Labeling algorithm

Abstract

Novel Sequence Generating Algorithm (SGA) and Potential Interval Qualifier Algorithm (PIQA) are designed to classify potential interval estimates of a given nonlinear equation into intervals possessing roots and intervals containing extrema. Using trisection method, SGA is developed to generate conjugate pair of sequences that converge to a point in the interval. Further, PIQA qualifies each interval into interval enclosing a root or interval containing extrema. If the interval contains a root, the multiplicity of root is also obtained. The proposed methodologies have been implemented and demonstrated through a set of benchmark functions to illustrate the effectiveness.