Matrizes e sistemas de equações lineares intervalares

Abstract

This work aims to approach fundamental mathematical concepts for the theory of Interval Analysis. The main object of study of the theory, instead of real numbers, is the use of closed intervals. Interval Analysis is a recent field of study, but it has been shown to be of great importance in the field of numerical methods as it allows more accurate results. Thus, the monograph initially addresses preliminary contents of the theory, such as interval operations of sets and interval arithmetic operations. Then, it presents some relationships and results about the content and interval functions as well as the Fundamental Theorem of Interval Analysis. Afterwards, the mathematical concept of interval matrices and linear systems of interval equations is discussed, focusing on the study of the solution of such systems and the differences between interval mathematics and usual mathematics. Ending the monograph with a possible application of the theory using interval polynomial interpolation to determine coefficients of an interval polynomial function with real variables using the Python programming language for code implementation.