A method to find all solutions of a system of multivariate polynomial equalities and inequalities in the max algebra


Reference:
B. De Schutter and B. De Moor, "A method to find all solutions of a system of multivariate polynomial equalities and inequalities in the max algebra," Discrete Event Dynamic Systems: Theory and Applications, vol. 6, no. 2, pp. 115-138, Mar. 1996.

Abstract:
In this paper we show that finding solutions of a system of multivariate polynomial equalities and inequalities in the max algebra is equivalent to solving an Extended Linear Complementarity Problem. This allows us to find all solutions of such a system of multivariate polynomial equalities and inequalities and provides a geometrical insight in the structure of the solution set. We also demonstrate that this enables us to solve many important problems in the max algebra and the max-min-plus algebra such as matrix decompositions, construction of matrices with a given characteristic polynomial, state space transformations and the (minimal) state space realization problem.


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Bibtex entry:

@article{DeSDeM:93-71,
        author={B. {De Schutter} and B. {De Moor}},
        title={A method to find all solutions of a system of multivariate polynomial equalities and inequalities in the max algebra},
        journal={Discrete Event Dynamic Systems: Theory and Applications},
        volume={6},
        number={2},
        pages={115--138},
        month=mar,
        year={1996},
        doi={10.1007/BF01797235}
        }



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