On the convergence of subproper (multi)-splitting methods for solving rectangular linear systems (Q931069)

The authors discuss iterative methods for solving consistent systems of linear equations \(Ax = b\), where \(A\) is a \(m \times n\) complex matrix. At first a necessary and sufficient condition for the convergence of the stationary iterative process \(x^{(k+1)} = M^+Nx^{(k)} + M^+b\) is derived, where \(A = M-N\) is a subproper splitting of the matrix \(A\) and \(M^+\) denotes the Moore-Penrose inverse of \(M\). Additionally, conditions for the equivalence of the convergence and quotient convergence for the stationary iterative process are given. Finally, the convergence of multi-splitting algorithms for rectangular systems is proved.