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The limited memory steepest descent method (LMSD) proposed by Fletcher is anextension of the Barzilai-Borwein "two-point step size" strategy for steepestdescent methods for solving unconstrained optimization problems. It is knownthat the Barzilai-Borwein strategy yields a method with an R-linear rate ofconvergence when it is employed to minimize a strongly convex quadratic. Thispaper extends this analysis for LMSD, also for strongly convex quadratics. Inparticular, it is shown that the method is R-linearly convergent for any choiceof the history length parameter. The results of numerical experiments areprovided to illustrate behaviors of the method that are revealed through thetheoretical analysis.

R-Linear Convergence of Limited Memory Steepest Descent