BibTeX
@TECHREPORT{Kolda97limited-memorymatrix,
author = {Tamara Gibson Kolda},
title = {Limited-Memory Matrix Methods with Applications},
institution = {},
year = {1997}
}
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Abstract
Abstract. The focus of this dissertation is on matrix decompositions that use a limited amount of computer memory � thereby allowing problems with a very large number of variables to be solved. Speci�cally � we will focus on two applications areas � optimization and information retrieval. We introduce a general algebraic form for the matrix update in limited�memory quasi� Newton methods. Many well�known methods such as limited�memory Broyden Family meth� ods satisfy the general form. We are able to prove several results about methods which sat� isfy the general form. In particular � we show that the only limited�memory Broyden Family method �using exact line searches � that is guaranteed to terminate within n iterations on an n�dimensional strictly convex quadratic is the limited�memory BFGS method. Further� more � we are able to introduce several new variations on the limited�memory BFGS method that retain the quadratic termination property. We also have a new result that shows that full�memory Broyden Family methods �using exact line searches � that skip p updates to the quasi�Newton matrix will terminate in no more than n�p steps on an n�dimensional strictly convex quadratic. We propose several new variations on the limited�memory BFGS method
