Combinatorial Canonical Form of Layered Mixed Matrices and Its Application to Block-Triangularization of Systems of Linear/Nonlinear Equations
Kazuo Murota, Masao Iri, Masataka Nakamura · SIAM Journal on Algebraic and Discrete Methods · 1987
With a view to obtaining an efficient procedure for solving large-scale systems of equations, canonical block-triangular forms are defined for layered mixed matrices and for mixed matrices, and some practical examples are presented. The canonical forms are obtained from a straightforward application of the decomposition principle for submodular functions. The relation to the existing decomposition techniques for electrical networks, as well as to the Dulmage–Mendelsohn decomposition, is also discussed.