Open AccessLinear Algebra and Differential Calculus in Pseudo-Intervals Vector Space
Author(s) -
Abdelouahab Kenoufi
Publication year - 2016
Publication title -
tema
Language(s) - English
Resource type - Journals
eISSN - 2179-8451
pISSN - 1677-1966
DOI - 10.5540/tema.2016.017.03.0283
Subject(s) - mathematics , differential calculus , linear algebra , vector space , algebra over a field , embedding , vector calculus , pure mathematics , calculus (dental) , mathematical analysis , computer science , geometry , medicine , dentistry , artificial intelligence
In this paper one proposes to use a new approach of interval arithmetic, the so-called pseudo- intervals [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.