A New Approach to Solve Linear Systems

Solving linear system is central to scientific computations. Given a linear system A x = b , where A is a non-singular real matrix. None of the existing solution approaches to the system is capable of exploiting special information provided by a proper sub-system. Only recently, Moradi et. al. (Nonlinear Dyn Syst Theory 19(1):193–199, 2019) showed that in the special case where corner minors of A are all non-zero, solutions to sub-systems generated by the corner sub-matrices of A could be used to construct a solution to the original system. In this paper, we extend the result to the case where no restriction is imposed on the coefficient matrix, A .