Fully Uncertain Linear Systems And Methods

With the development of science and engineering technology,the general linear systems in linear algebra have been unable to meet the requirements of research and applications.Linear systems with uncertain variables have attracted some researchers’attention.Li and Zhu proposed the concept of uncertain linear systems and gave the corresponding solving formula in 2014.Base on it,the concept of fully uncertain linear systems(or fully uncertain linear equations)is defined in this paper.Furthermore,we discuss the sufficient conditions of the solution to the fully uncertain linear systems.For the case of the coefficients of a system are square and non-square,we give the formulas to find the solution of this system as well as in what conditions to guarantee solutions in this paper.Taking into account of the difficulty of computing inverse matrix and the large calculation,this paper discusses the numerical iterative algorithms for the fully uncertain linear systems and the convergence of those numerical iterative algorithms.Finally,several numerical examples and an application example are presented for the fully uncertain linear systems.