On the convergence of splittings for semidefinite linear systems (Q952045)

The authors refer to the classical notion of P-regularity, introduced by \textit{H. B. Keller} [J. Soc. Ind. Appl. Math., Ser. B Numer. Anal. 2, 281--290 (1965; Zbl 0135.37503)] for the solution of singular and semidefinite linear systems by iteration. In this respect they consider stipulations on a splitting \(A=M-N\), which lead to fixed point systems such that the iterative scheme converges to a weighted Moore-Penrose solution of the system. Their result requires less restrictions on the splittings that Keller's P-regularity condition to ensure convergence of the iteration.