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Smith normal form using scaled extended integer ABS algorithms

Golpar Raboky, E ; Sharif University of Technology | 2012

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  1. Type of Document: Article
  2. DOI: 10.1007/978-3-642-28308-6_50
  3. Publisher: 2012
  4. Abstract:
  5. 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
  6. Keywords:
  7. Diophantine equation ; Integer Linear Programming ; Integer matrices ; Nonsingular ; Null space ; Numerical results ; Smith normal form ; Systems of equations ; Test problem ; Unimodular ; Algorithms ; Computer applications ; Linear systems ; Matrix algebra
  8. Source: Advances in Intelligent and Soft Computing ; Volume 145 AISC, Issue VOL. 2 , 2012 , Pages 367-372 ; 18675662 (ISSN)
  9. URL: http://link.springer.com/chapter/10.1007%2F978-3-642-28308-6_50