Publica
Hier finden Sie wissenschaftliche Publikationen aus den FraunhoferInstituten. On systems of linear equations with nonnegative coefficients
 Applicable algebra in engineering, communication and computing 14 (2004), No.6, pp.397414 ISSN: 09381287 ISSN: 09381279 

 English 
 Journal Article 
 Fraunhofer HHI () 
Abstract
We consider a system of linear equations with positive coefficients, where the entries of the nonnegative irreducible coefficient matrix depend on a parameter vector. We say that the parameter vector is feasible if there exists a positive solution to this system. A set of all feasible parameter vectors is called the feasibility set. If all the positive entries are logconvex functions, the paper shows that the associated Perron root is logconvex on the parameter set and the l1norm of the solution is logconvex on the feasibility set. These results imply that the feasibility set is a convex set regardless whether the l1norm of the solution is bounded by some positive real number or not. Finally, we show important applications of these results to wireless communication networks and prove some other interesting results for this special case.the paper shows that the associated Perron root is logconvex on the parameter set and the l1norm is logconvex on the feasibility set. These results imply that the feasibility set is a convex set regardless whether the l1norm is bounded by some positive real number or not. Finally, we show important applications of these results to wireless communication networks and prove some other interesting results for this special case.