THE NEWTON-RAPHSON METHOD OF REAL-VALUED FUNCTIONS IN DISCRETE METRIC SPACE

Abstract

This paper studies the Newton-Raphson method to approximate a root of a real-valued function in one-dimensional real discrete metric space. The method involves a derivative and is considered to be convergent very fast. However, the derivative is derived from the limit definition with respect to the Euclidean distance, different from that of the discrete metric space. This research investigates the Newton-Raphson method with respect to derivatives defined in discrete metric spaces by deriving the derivative first. The results show that the constructed Newton-Raphson method can be an alternative root-finding method exemplified by some examples.
 Keywords: Newton-Raphson method, discrete metric space, metric space derivative