Viewing a response to: @xeliram/ecuaciones-diofanticas-lineal. spanish · @ · 58 days ago. @xeliram, go and place your daily vote for Steem on . Optimización por Enjambre de Partículas Discreto en la Solución Numérica de un Sistema de Ecuaciones Diofánticas Lineales. Iván Amaya a, Luis Gómez b. Ecuaciones diofánticas lineales, soluciones cor- tas, algoritmo de reducción de la base. 1. Introduction. One can solve the linear Diophantine equation. aT x = b.

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During all the examples, the following parameters were used: Addison-Wesley, Boston, [7] Abraham, S.

A basic result of the mathematical analysis of the algorithm establishes that if is a compact set i. Absolute Value Programming O. The first one is a vector of random numbers, initially, in a valid solution interval.

Ecuaciones diofánticas lineales. Tabla con algoritmo de Euclides.

Implementation of kalman filter for the indoor location system of a lego nxt mobile robot. Simple problems are used to show its efficacy.

According to theorem 1, in order for the system 6 to have a solution, it is necessary, but not sufficient, that each of the equations have a solution; this is equivalent to establishing if for each it holds that divides. Vector Spaces Mathematics Course Two factorizations of an element of B are regarded as essentially the same if. Now, for g to be continuous in X it is enough that each f i is continuous in X.

However, in this case they do not have a solution in the set of integers, e. Some authors have previously proposed the solution of a Diophantine equation through artificial intelligence algorithms [6], [7].

Abstract This article proposes the use of a discrete version of the well known Particle Swarm Optimization, DPSO, a metaheuristic optimization algorithm for numerically solving a system of linear Diophantine equations. Then, if for a region of the plane can be determined, where a global minimum of functiondefined by 5and its value is zero, then any global minimizer with integer coordinates, should it ecuqciones, serves as a particular solution of eq.


Se utilizan algunos problemas sencillos para verificar su eficacia.

Linear Diophantine equations; objective function; optimization; particle swarm. Likewise, the transformation of this type of problem i.

Ecuaciones diofánticas lineales. Tabla con algoritmo de Euclides.

It is worth mentioning that it was not possible to find these roots by using commercial software nor through traditional means. February 25 th Moreover, it was found that the convergence time and the number of iterations are random variables that mainly depend on factors such as the algorithm parameters, the initial swarm and the linealds of the system.

Substracting the fourth and fifth equations, is obtained, which means that. The chapter More information. Therefore, for the function defined in 9 linealds, if there does not exist a global minimum in or if it exists but is different from zero, then the system of equations 8 does not have a solution in.

Ecuaciones Diofánticas by Otto Mauricio Sajchè on Prezi

The general condition of the theorem 4 about the feasibility of solving the system ecuafiones is important, since it is possible that the function g defined in 9 can be globally minimized but that the system 8 does not have a solution. After some preliminary results, we specialize More information.

It can then be concluded that, for this system, the algorithm delivers an answer with excellent precision and accuracy, even though the number of iterations and the duration were variable. An algorithm, considered as a variant of the traditional PSO, was used, [9]. Thus, the problem of determining whether a linear Diophantine equation has a solution or not, is reduced to showing if the greatest common divisor of the a i coefficients divide b or not.


How to find all solutions to a linear Diophantine More information. A first stage is given by the random assignation of a swarm of user defined integers. April 3 th It is said that the integers are a solution for eq. Moreover, there is a strong mathematical foundation for this type of equations and their solutions both, at a fundamental and at an applied level.

Animal Biodiversity and Conservation Also, it was observed that it is possible to solve this optimization problem without using conventional approaches. Tools and Diophantine Equations and Vol. March received More information. However, in case that it is required to solve a system with more unknowns than equations, a typical situation, they are out of the question.

Springer-Verlag, New York, It was shown, through some simple examples, that, at least for these systems, solutions with high precision and accuracy are achieved. The second one can also be a random vector, but it can be assumed as zero for the first iteration, in order to keep it simple.

Likewise, if the system is of a considerable size, the convergence time drastically increases, since a big search domain is required a case found during the current researchso the numerical strategy proposed here gains importance as a possible solution alternative. Two factorizations of an element of B are regarded as essentially the same if More information. Thus, the last equation provides.