Solution of large linear systems with embedded network structure for a non-homogeneous network flow programming problem

Details Solution of large linear systems with embedded network structure for a non-homogeneous network flow programming problem Solution of large linear systems with embedded network structure for a non-homogeneous network flow programming problem

2008-07-03

arxiv.org/abs/0807.0549v1

Mathematics

Optimization and Control

accepted in Mathematica Balkanica

Scientific paper

In the paper we consider the linear underdetermined system of a special type. Systems of this type appear in non-homogeneous network flow programming problems in the form of systems of constraints and can be characterized as systems with a large sparse submatrix representing the embedded network structure. We develop a direct method for finding solutions of the system. The algorithm is based on the theoretic-graph specificities for the structure of the support and properties of the basis of a solution space of a homogeneous system. One of the key steps is decomposition of the system. A simple example is regarded at the end of the paper.

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