Iterative solution of simultaneous equations

摘要

Stationary linear iteration methods are used to obtain generalized solutions for simultaneous equations. In particular the case is considered that the iterates terminate after finitely many steps. On the other side also the case is pointed out that the iterates converge, but not to a generalized solution. The well known method of Kaczmarz arises as a special case. Finally, the connection to matching rules is set up, which appear in the asymptotic theory of singular perturbations.