Stud. Univ. Babe¸ s-Bolyai Math. 59(2014), No. 4, 533–542 Enclosing the solution set of overdetermined systems of interval linear equations Szilvia Husz´ arszky and Lajos Gerg´ o Abstract. We describe two methods to bound the solution set of full rank interval linear equation systems Ax = b where A ∈ IR m×n , m ≥ n is a full rank interval matrix and b ∈ IR m is an interval vector. The methods are based on the concept of generalized solution of overdetermined systems of linear equations. We use two type of preconditioning the m × n system: multiplying the system with the generalized inverse of the midpoint matrix or with the transpose of the midpoint matrix. It results an n × n system which we solve using Gaussian elimination or the method provided by J. Rohn in [8]. We give some examples in which we compare the efficiency of our methods and compare the results with the interval Householder method [11]. Mathematics Subject Classification (2010): 65G06. Keywords: Interval linear equation, overdetermined, preconditioning. 1. Introduction An interval matrix, A, is a matrix whose elements are intervals, an interval vector, b, is a vector whose components are intervals. Let A =[A , A] be an m × n interval matrix and b =[b , b] an m-dimensional interval vector. We suppose that m ≥ n and the interval matrix A has full rank, i.e., all real matrices A ∈ A have full rank. Consider the set of linear equations Ax = b. (1.1) The set of solutions of such problem is given by  (A, b)=   x ∈ R n |∃A ∈ A, ∃b ∈ b : ‖A x − b‖ = min x∈R n ‖Ax − b‖  , i.e., the minimalization of ‖Ax − b‖ for any A ∈ A and any b ∈ b. This paper was presented at the 10th Joint Conference on Mathematics and Computer Science (MaCS 2014), May 21-25, 2014, Cluj-Napoca, Romania.