K-矩阵的组合特征
Combinatorial Characterizations of K-matrices
摘要：
给出了K-矩阵的若干组合刻画。这将Fiedler和Ptak关于K-矩阵的线性代数特征的一个定理推广到定向拟阵的情形。我们的证明是基本的，并大大简化了原来的证明，利用定向拟阵的对偶性。作为应用，我们证明了一个简单的主枢轴方法适用于线性互补性问题与K-矩阵收敛非常快，由一个纯粹的组合参数。
英文摘要：
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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