Abstract
Recently, we described a generalization of Rosser’s algorithm for a single linear Diophantine equation to an algorithm for solving systems of linear Diophantine equations. Here, we make use of the new formulation to present a new algorithm for solving rank one perturbed linear Diophantine systems, based on using Rosser’s approach. Finally, we compare the efficiency and effectiveness of our proposed algorithm with the algorithm proposed by Amini and Mahdavi-Amiri (Optim Methods Softw 21:819–831, 2006).
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References
Anderson IT (1972) Elementary rings and modules. Oliver and Boyd, Edinburgh
Amini K, Mahdavi-Amiri N (2006) Solving rank one perturbed linear Diophantine systems by the ABS method. Optim Methods Softw 21: 819–831
Anderson FW, Fuller KR (1992) Rings and categories of modules (graduate texts in mathematics). Springer, New York
Cassels JWS (1997) An introduction to the geometry of numbers. Springer, Berlin
Chou TJ, Collins GE (1982) Algorithms for the solutions of systems of linear Diophantine equations. SIAM J Comput 11: 686–708
Esmaeili H, Mahdavi-Amiri N, Spedicato E (2001) A class of ABS algorithms for Diophantine linear systems. Numer Math 90: 101–115
Khorramizadeh M, Mahdavi-Amiri N (2008) On solving linear Diophantine systems using generalized Rosser’s algorithm. Bull Iran Math Soc 34: 1–25
Rosser B (1941) A note on the linear Diophantine equation. Am Math Monthly 48: 662–666
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Khorramizadeh, M., Mahdavi-Amiri, N. An efficient algorithm for solving rank one perturbed linear Diophantine systems using Rosser’s approach. 4OR-Q J Oper Res 9, 159–173 (2011). https://doi.org/10.1007/s10288-010-0152-6
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DOI: https://doi.org/10.1007/s10288-010-0152-6