On Solving Linear Diophantine Systems Using Generalized Rosser's Algorithm

on solving linear diophantine systems using generalized rosser's algorithm

On Solving Linear Diophantine Systems Using Generalized Rosser’s Algorithm

A difficulty in solving linear Diophantine systems is the rapid growth of intermediate results. Rosser’s algorithm for solving a single linear Diophatine equation is an efficient algorithm that effectively controls the growth of intermediate results. Here, we propose an approach to generalize Rosser’s algorithm and present two algorithms for solving systems of linear Diophantine equations. Then...

on solving linear diophantine systems using generalized rosser's algorithm

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Polyhedral Omega: A New Algorithm for Solving Linear Diophantine Systems

Polyhedral Omega is a new algorithm for solving linear Diophantine systems (LDS), i.e., for computing a multivariate rational function representation of the set of all non-negative integer solutions to a system of linear equations and inequalities. Polyhedral Omega combines methods from partition analysis with methods from polyhedral geometry. In particular, we combine MacMahon’s iterative appr...

Solving Linear Diophantine Equations

An overview of a family of methods for nding the minimal solutions to a single linear Diophantine equation over the natural numbers is given. Most of the formal details were dropped, some illustrations that might give some intuition on the methods being presented instead.

Generalized Capacitance Matrix Theorems and Algorithm for Solving Linear Systems

The capacitance matrix method has been widely used as an efficient numerical tool for solving the boundary value problems on irregular regions. Initially, this method was based on the Sherman–Morrison–Woodbury formula, an expression for the inverse of the matrix (A + UV ) with A ∈ <n×n and U,V ∈ <n×p. Extensions of this method reported in literature have made restrictive assumptions on the matr...