A note on an iterative method for generalized inversion of matrices
1966; American Mathematical Society; Volume: 20; Issue: 95 Linguagem: Inglês
10.1090/s0025-5718-66-99922-4
ISSN1088-6842
Autores Tópico(s)Iterative Methods for Nonlinear Equations
Resumo(1X) 7k+l = Xk(2PR(A) AXk) (k = 0, 1, .*) where Xo is an n X m complex matrix satisfying (2) Xo = A*Bo, Bo some nonsingular m X m matrix, (3) Xo = CoA*, CO some nonsingular n X n matrix, (4) AXoPR(A) < 1, (II fl any matrix norm [3]), (5) XoA PR(A*) || < 1, converges to the generalized inverse A+ of A. As pointed out in [1], the computational significance of the method (1) is limited by the need for knowledge of PR(A) (and of PR(A*) if condition (5) is to be checked). This difficulty is evaded in the following theorem. THEOREM 2. Let A be an arbitrary (nonzero) complex m X n matrix of rank r and let
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