Solving Interval Linear Equations

This paper considers the problem of finding x, x in Rⁿ such that x G- 1 h x for any G in Rn × n and h in Rⁿ with A G A and b h b, where inequalities are understood componentwise and A, A, b, b are given. It introduces a new iteration for computing an x and x. This iteration dominates the iteration commonly recommended in the literature in that its limiting [ x , x ] is always contained in the limiting one from the conventional iteration and it seems to converge faster in practice. The [ x , x ] from either iteration is optimal to first order in a strong sense.