**ABSTRACT**
### The finite section method and problems in frame theory

#### Ole Christensen and Thomas Strohmer

The finite section method is a convenient tool for
approximation of the inverse of certain operators using finite-dimensional
matrix techniques. In this paper we demonstrate that the method is very
useful in frame theory: it leads to an efficient approximation of the
inverse frame operator and also solves related computational problems in
frame theory. In the case of a frame which is localized w.r.t. an
orthonormal
basis we are able to estimate the rate of approximation.
The results are applied to the reproducing kernel
frame appearing in the theory for shift-invariant spaces generated by a
Riesz basis.

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