  Using exact computer arithmetic, it is possible to determine the (exact)
solution of a numerical model without rounding error. For such purposes, a
corresponding system of equations should be exactly defined, either directly or
by rationalisation of numerically given input data. In the latter case there is
an initial round off error, but this does not propagate during the solution
process. If this system is first exactly solved, then by the floating-point
arithmetic, convergence of the numerical method is easily followed. As one
example, IRM-CG, a special case of the more general Iterated Ritz method and
interesting replacement for a standard or preconditioned CG, is verified.
Further, because the computer demands and execution time grow enourmously with
the number of unknowns using this strategy, the possibilities for larger
systems are also provided.
