An Efficient Incremental Algorithm for Solving Systems of Linear Diophantine Equations

An Efficient Incremental Algorithm for Solving Systems of Linear Diophantine Equations

In this paper, we describe an algorithm for solving systems of linear Diophantine equations based on a generalization of an algorithm for solving one equation due to Fortenbacher 3]. It can solve a system as a whole, or be used incrementally when the system is a sequential accumulation of several subsystems. The proof of termination of the algorithm is diicult, whereas the proofs of completenes...

On Solving Linear Diophantine Systems Using Generalized Rosser's Algorithm

An efficient technique for solving systems of integral equations

In this paper, the wavelet method based on the Chebyshev polynomials of the second kind is introduced and used to solve systems of integral equations. Operational matrices of integration, product, and derivative are obtained for the second kind Chebyshev wavelets which will be used to convert the system of integral equations into a system of algebraic equations. Also, the error is analyzed and ...

An Efficient Numerical Algorithm For Solving Linear Differential Equations of Arbitrary Order And Coefficients

Referring to one of the recent works of the authors, presented in~cite{differentialbpf}, for numerical solution of linear differential equations, an alternative scheme is proposed in this article to considerably improve the accuracy and efficiency. For this purpose, triangular functions as a set of orthogonal functions are used. By using a special representation of the vector forms of triangula...

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.