Abstract
A primal-dual framework of combinatorial relaxation algorithms is proposed for computing the highest degree of a minor of order k of a rational function matrix. The algorithm can be used for computing the index of nilpotency of a matrix pencil (or the index of the associated differential algebraic equation). It is a linear algebraic version of the Hungarian method for the assignment problem. The proposed framework stands in contrast to the previous combinatorial relaxation algorithm based on weighted matchings, and may also be regarded as an extension of the Wolovich algorithm for row/column properness. Several algorithms are evaluated through computer experiments.
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