A frame allows every element in a Hilbert space H to be written as a Linear
combination of the frame elements, with coefficients called frame coeffici
ents. Calculation of the frame coeffrcients requires inversion of an operat
or S on H. We show how the inverse of S can be approximated as close as we
like using finite-dimensional linear algebra. In contrast with previous met
hods, our approximation can be used for any frame. Various consequences for
approximation of the frame coefficients or approximation of the solution t
o a moment problem are discussed. We also apply the results to Gabor frames
and frames consisting of translates of a single function. (C) 2000 Academi
c Press.