An ISS and l-stability approach to forward error analysis of iterative numerical algorithms

In this paper we have used results from ISS and lοο stability theory to find a systematic way of finding bounds on the forward error and the maximum finite precision error. The proposed approach is applied on the successive iteration method and the classical iterative methods. The obtained forward error bound is numerically observed to be tighter than the bounds given in the numerical analysis literature. Moreover, in contrast to bounds in the numerical analysis literature for the successive iteration method, the bound obtained using a control approach does not involve the solution of the problem. Although the proposed scheme provides a new systematic way for forward error analysis, we note that the conditions of ISS and lοο-stability might be restrictive and not all algorithms will satisfy them.