Análise Intervalar

Abstract

This monograph deals with some fundamental concepts of Interval Analysis and its applications. The core concept of this theory is dealing with variables given by closed intervals instead of real numbers. Interval Arithmetic is highly relevant for the development of numerical methods with reliable results, since it allows the accurate analysis of error propagation. Based on this, this monograph addresses the interval operations of sets. Then it discusses the basic arithmetic operations and their properties, comparing them to similar set theory operations. It also studies the main concepts of functions, intervals and their main results. After that, it presents the limits of sequences of interval numbers and interval functions to introduce finite convergence. In particular, it highlights the embedded interval sequences, in order to introduce convergent numerical methods. It wraps up by exploring some applications and possible uses of this arithmetic, using the Interval Bissection Method and Interval Newton Method, to determine real roots using codes implemented in the GNU Octave language.