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Title: Sparse linear systems: Theory of decomposition, methods, technology, applications and implementation in Wolfram Mathematica

In this paper we propose the theory of decomposition, methods, technologies, applications and implementation in Wol-fram Mathematica for the constructing the solutions of the sparse linear systems. One of the applications is the Sensor Location Problem for the symmetric graph in the case when split ratios of some arc flows can be zeros. The objective of that application is to minimize the number of sensors that are assigned to the nodes. We obtain a sparse system of linear algebraic equations and research its matrix rank. Sparse systems of these types appear in generalized network flow programming problems in the form of restrictions and can be characterized as systems with a large sparse sub-matrix representing the embedded network structure.
Authors:
 [1] ;  [2]
  1. Belarussian State University, 220030 Minsk, 4, Nezavisimosti avenue, Republic of Belarus (Belarus)
  2. The Natural Resources and Environmental Protestion Ministry of the Republic of Belarus, 220004 Minsk, 10 Kollektornaya Street, Republic of Belarus (Belarus)
Publication Date:
OSTI Identifier:
22494300
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 1690; Journal Issue: 1; Conference: AMEE '15: 41. international conference on applications of mathematics in engineering and economics, Sozopol (Bulgaria), 8-13 Jun 2015; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGEBRA; DECOMPOSITION; DIAGRAMS; EQUATIONS; GRAPH THEORY; IMPLEMENTATION; MATHEMATICAL SOLUTIONS; MATRICES; PROGRAMMING; SENSORS; SYMMETRY; TUNGSTEN