In this paper we generalize the discrete Fourier-Ricatti-Bessel transform, allowing, via choice of several appropriate parameters, the recovery of the discrete Fourier sine transform, the discrete Hankel transform, and the discrete Fourier-Ricatti-Bessel transform for all three classes of boundary conditions, and the associated asymptotic inversion formulas. We then numerically and analytically estimate the error in our discrete inversion formula, finding that the error decreases as the square of the size of the transform matrix. Finally, we apply our new transform to selected functions for which the continuous transform is known, compute the discrete backward transform, and asymptotically recover the original function.
|Commitee:||Dougherty, Anne, Goodrich, Robert K., Packer, Judith, Walter, Marty|
|School:||University of Colorado at Boulder|
|School Location:||United States -- Colorado|
|Source:||DAI-B 71/10, Dissertation Abstracts International|
|Subjects:||Mathematics, Theoretical Mathematics|
|Keywords:||Discrete formula, Fourier-Riccati-Bessel transform, Robin boundary conditions, Transform matrix, Transforms|
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