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Abstract
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
C.R. Category::
∗Project 19901006 supported by National Natural Science Foundation of China and Science Foundation of Laboratory of Computational Physics.
‡Supported by the State Major Key Project for Basic Researches in China.
∗Project 19901006 supported by National Natural Science Foundation of China and Science Foundation of Laboratory of Computational Physics.
‡Supported by the State Major Key Project for Basic Researches in China.
Notes
∗Project 19901006 supported by National Natural Science Foundation of China and Science Foundation of Laboratory of Computational Physics.
‡Supported by the State Major Key Project for Basic Researches in China.