Year: 1965
Type: article
Abstract: The iterative process, X+ = Xn(21 AX.), for computing A-1, is generalized to obtain the generalized inverse. An iterative method for inverting a matrix, due to Schulz [1], is based on the convergence of the sequence of matrices, defined recursively by (1) X,+1 = X,(21 AXn) (n = 0, 1, **) to the inverse A` of A, whenever X0 approximates A-'. In this note the process (1) is generalized to yield a sequence of matrices converging to A+, the generalized inverse of A [2]. Let A denote an n X n complex matrix, A* its conjugate transpose, PR(A) the perpendicular projection of Em on the range of A, PR(A.) the perpendicular projection of En on the range of A*, and A+ the generalized inverse of A. THEOREM. The sequence of matrices defined by (2) XYn+1 X.(2PR(4) AX,) (t = 01, Received November 9,1964. This content downloaded from 157.55.39.220 on Fri, 02 Sep 2016 04:12:02 UTC All use subject to http://about.jstor.org/terms
Source: Mathematics of Computation
Authors: R. B. Kellogg, J. Spanier
Language: English
Topic: Matrix Theory and Algorithms
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2018574635