Date of Award
Mathematics and Statistics
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In this thesis we develop and test a computational procedure which serves as a pre-processor for algorithms that are used to identify a frame for a pointed finite polyhedral cone generated by a finite set of non-negative vectors. The frame identification algorithms to which we apply our pre-processor are those that test membership in a frame by checking the feasibility of a certain system of linear equations with non-negativity restrictions on the variables. The effect of our pre-processor is two-fold. First, it provides a technique which, we hypothesize, quickly identifies some members of a frame. This avoids the expensive feasibility test for each member so identified. Second, it selects a subset of the generators which, we further hypothesize, is effective in the determination of frame membership of many of the generators through a feasibility check for a much smaller linear system. Our hypotheses are corroborated with some numerical testing. We also show how our pre-processor can be modified to the frame identification problem in Data Envelopment Analysis. These frame elements identify the so called efficient Decision Making Units of an organization. Finally, we use the connection to linear redundancy to suggest how results in that discipline can give further improvements to the frame identification problems.Dept. of Economics, Mathematics, and Statistics. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2000 .S51. Source: Masters Abstracts International, Volume: 40-03, page: 0715. Advisers: R. J. Caron; Y. P. Aneja. Thesis (M.Sc.)--University of Windsor (Canada), 2000.
Shaheen, Mahboob., "Frame of a pointed finite polyhedral cone." (2000). Electronic Theses and Dissertations. 2154.