Approximate quasi-Newton methods

We consider the effect of approximation on performance of quasi-Newton methods for infinite dimensional problems. In particular we study methods in which the approximation is refined at each iterate. We show how the local convergence behavior of the quasi-Newton method in the infinite dimensional setting is affected by the refinement strategy. Applications to boundary value problems and integral equations are considered.The research of this author was supported by NSF grant DMS-8601139 and AFOSR grant AFOSR-ISSA-860074.