Enclosing the solution set of overdetermined systems of interval linear equations

We describe two methods to bound the solution set of full rank interval linear equation systems Ax = b where A 2 IRmxn, m >= n is a full rank interval matrix and b is an element of IRm 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 x 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 x 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].