Matrix computations (3rd ed.)
Iterative Methods for Toeplitz Systems (Numerical Mathematics and Scientific Computation)
Iterative Methods for Toeplitz Systems (Numerical Mathematics and Scientific Computation)
Analysis of Toeplitz Operators (Springer Monographs in Mathematics)
Analysis of Toeplitz Operators (Springer Monographs in Mathematics)
The finite section method and problems in frame theory
Journal of Approximation Theory
Double Preconditioning for Gabor Frames
IEEE Transactions on Signal Processing
Dual Gabor frames: theory and computational aspects
IEEE Transactions on Signal Processing
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In this paper we show that frame coefficients related to Riesz bases of integer-translates are solutions of bi-infinite invertible Toeplitz systems. Hence the corresponding frame coefficients may be obtained by solving Toeplitz system directly, without complicated calculation of the inverse frame operator. We apply the finite section method to Toeplitz operator and provide a bi-directional Levinson algorithm to approximate solutions of biinfinite Toeplitz system, whose convergence is guaranteed by the recursive nature and properties of finite section method. Other advantages of the algorithm are the modest computational cost and less storage requirement.