Equations for Which Newton's Method Never Works: Pedagogical Examples

Authors

Leobardo Valera, The University of Texas at El PasoFollow
Martine Ceberio, The University of Texas at El PasoFollow
Olga Kosheleva, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

4-2020

Comments

Technical Report: UTEP-CS-20-31

Abstract

One of the most widely used methods for solving equations is the classical Newton's method. While this method often works -- and is used in computers for computations ranging from square root to division -- sometimes, this method does not work. Usual textbook examples describe situations when Newton's method works for some initial values but not for others. A natural question that students often ask is whether there exist functions for which Newton's method never works -- unless, of course, the initial approximation is already the desired solution. In this paper, we provide simple examples of such functions.