When I review papers with such assertions, here is what I look for:
A clear description of the problem, and any known features of the quantity one is interested in (unique root, local minimizer, etc);
A clear description of the method used;
Information on the stopping/ error criteria used. This latter is rather important - one may stop an algorithm when the successive approximations are 'close' in some norm, or when some residual measure is smaller than some threshold (presuming one's not exceeded a specified total number of iterations.)
With this information, and a sufficiently modest claim "the computed quantity 'a' appears to provide a good approximation to the desired result'', this reviewer would be happy.