Combinatorial Characterizations of K-matrices

Details Combinatorial Characterizations of K-matrices Combinatorial Characterizations of K-matrices

2009-11-11

arxiv.org/abs/0911.2171v3

Linear Algebra Appl., 434, pp. 68-80, 2011

Mathematics

Optimization and Control

17 pages; v2, v3: clarified proof of Thm 5.5, minor corrections

Scientific paper

10.1016/j.laa.2010.08.008

We present a number of combinatorial characterizations of K-matrices. This extends a theorem of Fiedler and Ptak on linear-algebraic characterizations of K-matrices to the setting of oriented matroids. Our proof is elementary and simplifies the original proof substantially by exploiting the duality of oriented matroids. As an application, we show that a simple principal pivot method applied to the linear complementarity problems with K-matrices converges very quickly, by a purely combinatorial argument.

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