Combinatorial Characterizations of K-matrices
arXiv:0911.2171 · doi:10.1016/j.laa.2010.08.008
Abstract
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.
17 pages; v2, v3: clarified proof of Thm 5.5, minor corrections