Vaughn Ellis

The sensitivity of linear systems is a question of great interest in numericalanalysis. Sensitive systems can lead to untrustworthy results. Traditionally,the condition number,, is used to measure the sensitivity of a system.However, in many scenarioscan be large when the solution is known tobe accurate. Alternatively, we can use the effective condition number,e.For a given linear system, theeoften gives a much better bound on error.This is especially true in numerical PDE’s. For example, it can be shownfor Poisson’s equation on the unit square solved through the finitedifference method (FDM) thate=O(1)and=O(h2), wherehis themaximal meshspacing. This talk will discusseand its utility to numericalPDE’s.