Software implementation of algorithm for solving a set of linear equations under interval uncertainty

We consider a set of linear equations $\mathbf Ax=\mathbf b$ with interval matrices $\mathbf A$, $\mathbf b$. Solutions are items of $\Theta_{tol}(\mathbf A,\mathbf b)=\{x:\mathbf Ax\in b\}$. Let $\Theta_{tol}(\mathbf A,\mathbf b(z))= \{x:\mathbf Ax=(1+z)\mathbf b)\}$, $z^* =\inf\{z: \Theta_{tol}(\mathbf A,\mathbf b(z))\ne\emptyset\}$ be. Items of the set $\Theta_{tol}(\mathbf A,\mathbf b(z^*))$ are referred to as pseudosolutions. We prove existence of a pseudosolution for all sets of interval algebraic linear equations, suggest a technique to search for the pseudosolution via solving the corresponding linear programming problem. The obtained problem is singular, thus computations demand accuracy exceeding that of standard data types of programming languages. Simplex method coupled with errorless rational-fractional computations gives an efficient solution of the problem. Coarsegrained parallelism for distributed computer systems with MPI gives a software implementation tool. CUDA C software is suggested for errorless rational-fractional calculations.