Marzieh Dehghani-Madiseh - Department of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, Iran

Generalized intervals (intervals whose bounds are not constrained to be increasingly ordered) extend classical intervals and present algebraic completion of conventional interval arithmetic, allowing efficient solution for interval linear systems. In this paper, we use the Cholesky decomposition of a symmetric generalized interval matrix {\bf{A}} introduced by Zhao et al. (A generalized Cholesky decomposition for interval matrix, Adv. Mat. Res. ۴۷۹ (۲۰۱۲) ۸۲۵--۸۲۸), to construct the algebraic solution of the triangular interval linear system of equations. Also we utilize this decomposition to find inner and outer estimations of the generalized solution set of the symmetric interval linear systems. Finally some numerical experiments and an application in economic are given to show the efficiency of the presented technique.

Interval arithmetic, Kaucher arithmetic, Cholesky decomposition