Abstract
Classes of integer ABS methods have recently been introduced for solving linear systems of Diophantine equations. The Smith normal form of a general integermatrix is a diagonal integer matrix, obtained by elementary nonsingular (unimodular) operations. Such a form may conveniently be used in solving integer systems of equations and integer linear programming problems. Here, we present a class of algorithms for computing the Smith normal form of an integer matrix. In doing this, we propose new ideas to develop a new class of extended integer ABS algorithms generating an integer basis for the integer null space of the matrix. Finally, we test our algorithms and report the obtained numerical results on randomly generated test problems.
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Golpar-Raboky, E., Mahdavi-Amiri, N. (2012). Smith Normal Form Using Scaled Extended Integer ABS Algorithms. In: Gaol, F., Nguyen, Q. (eds) Proceedings of the 2011 2nd International Congress on Computer Applications and Computational Science. Advances in Intelligent and Soft Computing, vol 145. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28308-6_50
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DOI: https://doi.org/10.1007/978-3-642-28308-6_50
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-28307-9
Online ISBN: 978-3-642-28308-6
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