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Solving linear systems over idempotent semifields through LU-factorization
- Source :
- Rendiconti del Circolo Matematico di Palermo Series 2.
- Publication Year :
- 2020
- Publisher :
- Springer Science and Business Media LLC, 2020.
-
Abstract
- In this paper, we introduce and analyze a new LU-factorization technique for square matrices over idempotent semifields. In particular, more emphasis is put on “max-plus” algebra here but the work is extended to other idempotent semifields as well. We first determine the conditions under which a square matrix has LU factors. Next, using this technique, we propose a method for solving square linear systems of equations whose system matrices are LU-factorizable. We also give conditions for an LU-factorizable system to have solutions. This work is an extension of similar techniques over fields. Maple® procedures for this LU-factorization are also included.
Details
- ISSN :
- 19734409 and 0009725X
- Database :
- OpenAIRE
- Journal :
- Rendiconti del Circolo Matematico di Palermo Series 2
- Accession number :
- edsair.doi...........2a2aa3e864e215d39816d4531d67362d