What do you mean by a solution to an operator equation

It is demonstrated that even the simplest integral equation in electromagnetics does not provide a numerically stable solution. The instability is not in the computation process but with the operator itself. Hence, when dealing with an ill-posed operator, the comparison of various entities such as error in the solution or in the residuals, for such problems has to be performed subjectively and not objectively. This makes code validation a rather difficult problem as there is no fixed guide to get the datum for an arbitrary problem.