For the solution of linear systems, the conjugate gradient (CG) and BFGS are among the most popular and successful algorithms with their respective advantages. The limited-memory methods have been developed to combine the best of the two. We describe and examine CG, BFGS, and two limited-memory methods (L-BFGS and VSCG) in the context of linear systems. We focus on the relationships between each of the four algorithms, and we present numerical results to illustrate those relationships.

Faculty Advisor Name

Michael P. Friedlander

Faculty Advisor Institution

University of British Columbia

Suggested Mathematics Subject Classification(s)

65K10, 90C53


The author would like to express his sincere gratitude and appreciation to his sponsor, Professor Michael Friedlander, for all the help and guidance throughout this project.

Included in

Mathematics Commons



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