On the Solution of Linear Algebraic Equations Involving Interval Coe cients

We discuss the solution to the interval algebraic systemA x b involving interval n n matrixA 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 A x 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