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.