Rank reduction processes for solving linear Diophantine systems and integer factorizations: a review

DOI10.1007/s41980-019-00282-8zbMath1452.65059OpenAlexW2974624174WikidataQ114217376 ScholiaQ114217376MaRDI QIDQ779712

Effat Golpar-Raboky, Nezam Mahdavi-Amiri

Publication date: 14 July 2020

Published in: Bulletin of the Iranian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s41980-019-00282-8

zbMATH Keywords

Smith normal formmatrix decompositionlinear Diophantine systemsinteger rank reduction formula

Mathematics Subject Classification ID

Factorization of matrices (15A23) Iterative numerical methods for linear systems (65F10) Matrices of integers (15B36) Linear equations (linear algebraic aspects) (15A06)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• WZ factorization via Abaffy-Broyden-Spedicato algorithms
• An efficient algorithm for solving rank one perturbed linear Diophantine systems using Rosser's approach
• The rank reduction procedure of Egerváry
• ABS methods for continuous and integer linear equations and optimization
• The WZ matrix factorisation method
• Generating the integer null space and conditions for determination of an integer basis using the ABS algorithms
• On rank-diminishing operations and their applications to the solution of linear equations
• A class of direct methods for linear systems
• On solving linear Diophantine systems using generalized Rosser's algorithm
• Integer extended ABS algorithms and possible control of intermediate results for linear Diophantine systems
• The rank of a difference of matrices and associated generalized inverses
• Using the Blankinship algorithm to find the general solution of a linear diophantine equation
• ABS methods and ABSPACK for linear systems and optimization: A review
• Diophantine quadratic equation and Smith normal form using scaled extended integer Abaffy-Broyden-Spedicato algorithms
• Extended rank reduction formulas containing Wedderburn and Abaffy-Broyden-Spedicato rank reducing processes
• Rank reduction, factorization and conjugation
• ABS solution of a class of linear integer inequalities and integer LP problems
• Extended integer rank reduction formulas and Smith normal form
• Solving rank one perturbed linear Diophantine systems by the ABS method
• Real and integer Wedderburn rank reduction formulas for matrix decompositions
• Algorithms for the Solution of Systems of Linear Diophantine Equations
• Implicit matrix elimination (IME) schemes
• The implicit LX method of the ABS class
• A Rank–One Reduction Formula and Its Applications to Matrix Factorizations
• A New Version of the Euclidean Algorith
• A Note on the Linear Diophantine Equation
• A class of ABS algorithms for Diophantine linear systems

This page was built for publication: Rank reduction processes for solving linear Diophantine systems and integer factorizations: a review