A Sign Function Approach to Solve Algebraically Interval System of Linear Equations for Nonnegative Solutions

Article type: Research Article

Authors: Chakraverty, Snehashish^{a; *} | Hladík, Milan^b | Mahato, Nisha Rani^c

Affiliations: [a] Department of Mathematics, National Institute of Technology Rourkela, Odisha, India. sne_chak@yahoo.com | [b] Department of Applied Mathematics, Faculty of Mathematics and Physics, Charles University, Malostranské nám. 25, 11800 Prague, Czech Republic. milan.hladik@matfyz.cz, hladik@kam.mff.cuni.cz | [c] Department of Mathematics, National Institute of Technology Rourkela, Odisha, India. nisha.mahato1@gmail.com

Correspondence: [*] Address for correspondence: Department of Mathematics, National Institute of Technology Rourkela, Odisha, India.

Abstract: This paper deals with solving interval system of linear equations. The problem is to find a nonnegative algebraic solution. Based on sign function approach and using interval center and radius arithmetic operations, we propose an algorithm for computation of an algebraic interval solution vector. We also discuss fundamental properties of this solution vector, such as existence and uniqueness. Further, the nonnegative solution algorithm has been extended to other sign-restricted approach. Numerical examples of interval system of linear equations show efficiency of the algorithms presented.

Keywords: Interval matrix, Interval analysis, Linear system of equations, Linear interval systems, Nonnegative solution

DOI: 10.3233/FI-2017-1510

Journal: Fundamenta Informaticae, vol. 152, no. 1, pp. 13-31, 2017