Frame of a pointed finite polyhedral cone.

TL;DRAbstract

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 b

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