Uncertainty in the solution of linear operator equations

Abstract

In this paper we introduce and explore the concept of uncertainty of an approximate solution of a linear operator equation. This uncertainty is a measure of the difference between a computed solution and other plausible answers. When the operator equation is wellposed, the uncertainty is closely related to the more traditional notion of the accuracy of an approximate solution. However, for illposed equations, the uncertainty concept gives a new way of looking at such problems and helps in assessing the meaning of the computed results.