The talk On GMRES for singular systems, by Miroslav Rozložník will be held on Monday April 24, 2017 at 9:00 in room K4.
In this talk we study the numerical behavior of the generalized minimal residual (GMRES) method for solving singular linear systems. GMRES determines a solution without breakdown in theory in the two cases: the coefficient matrix is symmetric in its range space (EP); its range space and null spaces are disjoint (GP). We show how the inconsistency of a linear system and the principal angles between the range o A and the range o A^T affect the conditioning of the extended Hessenberg matrix in the Arnoldi decomposition and the accuracy of computed iterates. We compare GMRES with the range restricted GMRES (RR-GMRES) method and the simpler GMRES method. Numerical experiments show typical behavior of GMRES in the EP and GP cases.