(T,S) splitting methods for computing the generalized inverse and rectangular systems

Given a real rectangular matrix A. In this paper the (T,S) splitting method of A = U- V such that R(U)=AT and for computing the generalized inverse is established. In consideration of the rectangular systems Au =f, we show that the sequence of the iterations converges to if and only if the spectral radius of is less than unity. The characteristics of the solution are developed. We present convergent conditions of the iteration matrix , and generalize the results of Coliatz and Marek and Szyld on monotone type iterations. Some criteria under regularity assumptions for comparing convergence rates of are given, where are (T,S) splittings of A

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