Projection methods solving rectangular systems of linear equations

摘要

This survey paper contains a general characterization of stationary and instationary linear iterative one-step methods solving over- or underdetermined linear algebraic systems, techniques for convergence acceleration, and some generalizations of the Kaczmarz (ART) and the De la Garza methods. Among others the question is answered, under what conditions an iteration process yields a generalized matrix inverse of the type A−, A(1,2), A(1,2,3), A(1,2,4), A+, respectively, and under what conditions the resulting limit vector is a minimum-norm-solution, a least-squares-solution or a solution of the initial linear system.