University of GuilanJournal of Mathematical Modeling2345-394X8420200901Inner and outer estimations of the generalized solution sets and an application in economic345361405810.22124/jmm.2020.16119.1409ENMarziehDehghani-MadisehDepartment of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran
University of Ahvaz, Ahvaz, IranJournal Article20200331Generalized 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. 479 (2012) 825--828), 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.https://jmm.guilan.ac.ir/article_4058_6f52e383583bbe79be4104c24973daa2.pdf