Geodesic
Existence and Computation of the Set of Positive Solutions to Polynomial Matrix Equations
International Journal of Applied Mathematics and Computer Science, Tome 10 (2000) no. 2, pp. 309-320.

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Necessary and sufficient conditions are established for the existence of positive solutions to polynomial diophatine equations. A method of computing of the set of positive solutions to a polynomial diophatine equation based on extreme points and extreme directions is proposed. The effectiveness of the method is demonstrated on a numerical example.
Keywords: computation, set of positive solutions, polynomial matrix equation
Mots-clés : obliczanie, równanie macierzowe 
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     author = {Kaczorek, T. and {\L}opatka, R.},
     title = {Existence and {Computation} of the {Set} of {Positive} {Solutions} to {Polynomial} {Matrix} {Equations}},
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Kaczorek, T.; Łopatka, R. Existence and Computation of the Set of Positive Solutions to Polynomial Matrix Equations. International Journal of Applied Mathematics and Computer Science, Tome 10 (2000) no. 2, pp. 309-320. http://geodesic.mathdoc.fr/item/IJAMCS_2000_10_2_a5/