Linear Algebra and Differential Calculus in Pseudo-Intervals Vector Space

Abstract

ABSTRACT. In this paper one proposes to use a new approach of interval arithmetic, the so-called pseudointervals [1,5,13]. It uses a construction which is more canonical and based on the semi-group completion into the group, and it allows to build a Banach vector space. This is achieved by embedding the vector space into free algebra of dimensions higher than 4. It permits to perform linear algebra and differential calculus with pseudo-intervals. Some numerical applications for interval matrix eigenmode calculation, inversion and function minimization are exhibited for simple examples.