For Solving Linear Diophantine Equations Abs Methods And Winabs03 Research

In 1984, Abaffy, Broyden and Spedicato developed a kind of projection algorithms for linear and nonlinear equations - ABS algorithms. Throughout the following twenty years, ABS algorithms have been extended to solve the least squares, the inequality systems, linear programming and nonlinear programming with linear constraints etc. Linear Diophantine equations appear often in modeling and practical application, which play an important part in transportation. So it is particularly necessary to find out the solution of linear diophantine equation. This paper is devoted to studying the linear diophantine equation systematically under the ABS environment.In this thesis, three parts are considered. Firstly we outline the development of ABS algorithms and the ABS software; Secondly, the approaches for linear Diophantine equations are illuminated in detail; Finally we present the LLIU algorithm and the IILX for linear Diophantine equations, at the same time my work in ABS software is given. The main results obtained in this thesis can be summarized as follows:1. In chapter two, we analyzed the methods for single linear Diophantine equations: Rosser algorithm and Fortenbacher algorithm; the methods for linear Diophantine equations: EMAS algorithm and Contejean algorithm.2. In chapter three, the DLU and IILX algorithms for linear Diophantine equations are given based on the ABS algorithms. Corresponding properties, complexity and their application are discussed.3. Chapter four improves the input interface, net page introduction and installation, the usage of WinABS03 and ABSDLL03 is presented.