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arXiv · 0911.2171

Combinatorial Characterizations of K-matrices

Jan Foniok·Komei Fukuda·Lorenz Klaus
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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.

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Jan Foniok, Komei Fukuda, Lorenz Klaus. 2009-11-11. Combinatorial Characterizations of K-matrices. https://doi.org/10.1016/j.laa.2010.08.008

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