On the convergence of an iterative method for the computation of generalized inverse and associated projections †

1 July 1971

journal article
research article
Published by Taylor & Francis in International Journal of Systems Science

Vol. 2 (1) , 67-75
https://doi.org/10.1080/00207727108920178

Abstract

An iterative method, with convergence of any desired finite order, for computing the generalized inverse A ⁺ and the associated projections AA ⁺ and A ⁺ A for any matrix A is developed. The method uses an upper bound on the maximum eigen-value of AAast; (or A∗A). It is also shown that the trace of a sequence of approximations to AA ⁺ (or A ⁺ A) converges to the rank of A. Finally, examples are given illustrating the computation of the generalized inverse and rank.

Keywords

This publication has 3 references indexed in Scilit:

On Best Linear Estimation and General Gauss-Markov Theorem in Linear Models with Arbitrary Nonnegative Covariance Structure
SIAM Journal on Applied Mathematics, 1969
On Iterative Computation of Generalized Inverses and Associated Projections
SIAM Journal on Numerical Analysis, 1966
A generalized inverse for matrices
Mathematical Proceedings of the Cambridge Philosophical Society, 1955