Iterative Consistency: A Concept for the Solution of Singular Systems of Linear Equations
Martin E. Hanke · SIAM Journal on Matrix Analysis and Applications · 1994
This paper deals with the computation of generalized solutions of singular linear systems of equations by semi-iterative methods. A new concept called iterative consistency is introduced to characterize linear fixed-point equations which lead to certain prescribed generalized solutions of the original problem. Several properties of this concept are discussed. Perturbations of such iteratively consistent fixed-point equations give rise to the computation of perturbed limit points. These approximants can still be interpreted as appropriate generalized solutions of the original system. Error expressions and first order derivatives are derived. The results are illustrated by the successive overrelaxation (SOR) and by the symmetric SOR (SSOR) method.