  The limited memory steepest descent method (LMSD) proposed by Fletcher is an
extension of the Barzilai-Borwein "two-point step size" strategy for steepest
descent methods for solving unconstrained optimization problems. It is known
that the Barzilai-Borwein strategy yields a method with an R-linear rate of
convergence when it is employed to minimize a strongly convex quadratic. This
paper extends this analysis for LMSD, also for strongly convex quadratics. In
particular, it is shown that the method is R-linearly convergent for any choice
of the history length parameter. The results of numerical experiments are
provided to illustrate behaviors of the method that are revealed through the
theoretical analysis.
