The ABS Method Of Solving Linear Equations And Inequality Systems

In 1984, Abaffy, Broyden and Spedicato developed a kind of pro-jection algorithms for linear and nonlinear equations-ABS algorithms.Throughout the following twenty years, ABS algorithms have beenextended to solve the least squares, the inequality systems, linear pro-gramming and nonlinear programming with linear constraints, etc.Linear Diophantine equations and inequations, especially over-determined linear inequations, appear often in practical application, whichplay an important role in the transportation. This paper is devoted tointroducing the linear Diophantine equations and inequations underthe ABS environment, and studying mainly a kind of ABS solving ofover-determined Linear inequations.In this thesis,three chapters are considered.The development ofABS algorithms and the ABS software are introduced in chapter one;Chapter two gives the basic ABS algorithm and some properties,and in-troduce a special kind of ABS algorithms-implicit LU algorithm.Themethods for linear Diophantine equations are analyzed, such as EMASalgorithm.Chapter three gives ABS algorithm for solving linear Dio-phantine inequations and their application in integer linear program-ming.A kind of ABS algorithm for solving over-determined linear in-equations is studied in detail in this chapter.Supplying the correspon-dence example and MATLAB programs for verifying.