Kennedy-Cochran-Patrick, Arthur (2022). Bounds for long max-plus matrix products. University of Birmingham. Ph.D.
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KennedyCochranPatrick2022PhD.pdf
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Abstract
We consider long matrix products over max-plus algebra and develop bounds on the transient of their length after which they admit a certain decomposition as the product length exceeds these bounds. First we build on the weak CSR approach for max-plus powers of a matrix by Merlet, Nowak, and Sergeev [68] and consider the case when the products are tropical matrix powers of just one matrix. For this case we obtain new bounds on the above mentioned transient that make use of the cyclicity of the associated digraph and the tropical factor rank. Next, we develop a CSR decomposition for tropical inhomogeneous matrix products and establish bounds in which certain matrix products become CSR. We also critically examine the limitations of the developed theory by presenting a number of counterexamples in the cases where no bound exists for a matrix product to be CSR.
| Type of Work: | Thesis (Doctorates > Ph.D.) | |||||||||
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| Award Type: | Doctorates > Ph.D. | |||||||||
| Supervisor(s): |
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| Licence: | All rights reserved | |||||||||
| College/Faculty: | Colleges (2008 onwards) > College of Engineering & Physical Sciences | |||||||||
| School or Department: | School of Mathematics | |||||||||
| Funders: | None/not applicable | |||||||||
| Subjects: | Q Science > QA Mathematics | |||||||||
| URI: | http://etheses.bham.ac.uk/id/eprint/12393 |
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