Let T denote an operator on a Hilbert space (H, [.,.]), and let {f(i)}(i=1)
(infinity) be a frame for the orthogonal complement of the kernel NT. We co
nstruct a sequence of operators {Phi (n)} of the form Phi (n) (.) = Sigma (
n)(i=1) [., g(t)(n)]f(i) which converges to the psuedo-inverse T+ of T in t
he strong operator topology as n --> infinity. The operators {Phi (n)} can
be found using finite-dimensional methods. We also prove an adaptive iterat
ive version of the result. (C) 2001 Academic Press.