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)
Zhiwei (Tony) Qin, The Relationships Between CG, BFGS, and Two Limited-memory Algorithms, Furman University Electronic Journal of Undergraduate Mathematics, 12 (2016), 5-20. Available at: http://scholarexchange.furman.edu/fuejum/vol12/iss1/2