A new approach to obtain algebraic solution of interval linear systems Authors T. Allahviranloo Department of Mathematics, Science and Research Branch Islamic Azad University M. Ghanbari Department of Mathematics, Science and Research Branch Islamic Azad University Original Paper

First Online: 03 June 2011 DOI :
10.1007/s00500-011-0739-7

Cite this article as: Allahviranloo, T. & Ghanbari, M. Soft Comput (2012) 16: 121. doi:10.1007/s00500-011-0739-7 Abstract In this paper, an algebraic solution of interval linear system involving a real square matrix and an interval right-hand side vector is obtained. A new approach to solve such systems based on the new concept “inclusion linear system” is proposed. Moreover, new necessary and sufficient conditions are derived for obtaining the unique algebraic solution. Furthermore, based on our method, an algorithm is proposed and numerically demonstrated. Finally, we compare the result obtained by our method with that obtained by interval Gauss elimination procedure.

Keywords Interval linear system Inclusion linear system Interval number vector Algebraic solution Solution set Fuzzy number

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