The use of the row block projection method (block Cimmino) for solving nonsymmetric linear system Ax = b gives rise to a symmetric positive definite system G x = g, where B is the sum of orthogonal projection matrices Pi = Ai(ATAi)-'AT, and where the Ar's are block rows of A. In this paper we present an efficient implementation of the cgT method for solving the derived symmetric positive defini...

Given a real matrix, we analyze an open interval, called row exclusion interval, such that the real eigenvalues do not belong to it. We characterize when the row exclusion interval is nonempty. In addition to the exclusion interval, inclusion intervals for the real eigenvalues, alternative to those provided by the Gerschgorin disks, are also considered for matrices whose off-diagonal entries pr...