Providing Meaningful Error Bounds for Solutions to Constrained Ill-Conditioned Linear Systems

Abstract

In this paper we compare the performance of several methods for providing tight error bounds for linearly constrained ill-posed linear equation solutions. Specifically, we compare accuracy and computational cost of three methods: suboptimal, SQP, and interior point method. We conclude from the experiments that the suboptimal method yields smooth but somewhat looser bounds than the interior point and SQP methods, but it typically has the best running time performance, especially for larger problems. The SQP method is suitable for small to medium size problems, yielding relatively low running times and stable, tight bounds. The interior point method is in general relatively expensive and produces highly erratic bounds for linear systems based on integral equations.