Block Gauss elimination followed by a classical iterative method for the solution of linear systems
Journal of Computational and Applied Mathematics
Convergence of General Nonstationary Iterative Methods for Solving Singular Linear Equations
SIAM Journal on Matrix Analysis and Applications
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New comparison theorems are presented comparing the asymptotic convergence factor of iterative methods for the solution of consistent (as well as inconsistent) singular systems of linear equations. The asymptotic convergence factor of the iteration matrix T is the quantity $\gamma(T) = \max \{ |\lambda| , \lambda \in \sigma(T), \lambda \neq 1\}$, where $\sigma(T)$ is the spectrum of T. In the new theorems, no restrictions are imposed on the projections associated with the two iteration matrices being compared. The splittings of the well-known example of Kaufman [ SIAM J. Sci. Statist. Comput., 4 (1983), pp. 525--552] satisfy the hypotheses of the new theorems.