A Comparison of Some Methods for Solving Linear Interval Equations∗

Certain cases in which the interval hull of a system of linear interval equations can be computed inexpensively are outlined. We extend a proposed technique of Hansen and Rohn with a formula that bounds the solution set of a system of equations whose coefficient matrix A = [A, A] is an H-matrix; when A is centered about a diagonal matrix, these bounds are the smallest possible (i.e., the bounds are then the solution hull). Hansen’s scheme also computes the solution hull when the linear interval system Ax = b = [b, b] is such that A is inverse positive and b = −b 6= 0. Earlier results of others also imply that, when A is an M-matrix and b ≥ 0,b ≤ 0, or 0 ∈ b, interval Gaussian elimination (IGA) computes the hull. We also give a method of computing the solution hull inexpensively in many instances when A is inverse positive, given an outer approximation such as that obtained from IGA. Examples are used to compare these schemes under various conditions.