Markov, S. M.; Popova, E. D.; Ullrich, C.: **On the Solution of
Linear Algebraic Equations Involving Interval Coefficients**
*Iterative Methods in Linear Algebra, II*, S. Margenov, P.
Vassilevski (Eds.) IMACS Series in Computational and Applied
Mathematics, **3** 1996, pp. 216-225.

We discuss the solution to the interval algebraic system **Ax = b**
involving interval matrix **A** and interval vector **b** in
directed interval arithmetic involving improper intervals. We give
some new relations for directed intervals, which form the basis for a
directed interval matrix algebra. Using such relations we prove
convergence of an iterative method, formulated by L. Kupriyanova,
under simple explicit conditions on the interval matrix **A**. We
propose an iterative numerical algorithm for the solution to a class
of interval algebraic systems **Ax = b**. Cramer-type formula for
a special case of real matrices and interval right-hand side are used
for the computation of an initial approximation for the iteration
method. A *Mathematica* function performing the proposed
algorithm is described.