Index Reduction via Unimodular Transformations

This paper presents an algorithm for transforming a matrix pencil A(s) into another matrix pencil U(s)A(s) with a unimodular matrix U(s) so that the resulting Kronecker index is at most one. The algorithm is based on the framework of combinatorial relaxation, which combines graph-algorithmic techniques and matrix computation. Our algorithm works for index reduction of linear constant coefficient differential-algebraic equations, including those for which the existing index reduction methods based on Pantelide's algorithm or the signature method are known to fail.