Abstract
A matroid-theoretic method is developed for the structural analysis of a system of equations under the more realistic situations than in Chapter 2. The matroid-theoretic characterization of the rank of a mixed matrix leads to the efficient algorithm for testing the structural solvability. The canonical forms of mixed matrices, bridging the LU-decomposition and the Dulmage-Mendelsohn decomposition, provide a powerful method for the hierarchical decomposition of a system of linear/nonlinear equations into subsystems.
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© 1987 Springer-Verlag Berlin Heidelberg
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Murota, K. (1987). Matroid-Theoretic Approach to the Solvability of a System of Equations. In: Systems Analysis by Graphs and Matroids. Algorithms and Combinatorics, vol 3. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-61586-3_6
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DOI: https://doi.org/10.1007/978-3-642-61586-3_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-17659-6
Online ISBN: 978-3-642-61586-3
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