Abstract
Generally the algorithms developed in this work are based on one- and multidimensional Fourier transforms and matrix inversions. During the last ten years much has been written in papers and books on the implementation of Fourier transforms and matrix inversions especially on multiprocessor architectures. Typically, large data sets are involved. The most time-consuming step in many computations is not arithmetic calculation but rather the complex global and local data reindexings needed to feed the Fourier transform and matrix inversion computations.
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A more complete treatment of the tensor product algebra can be found in the author’s text [51]. The text emphasizes the role of the tensor product in structuring 1-dimensional FFT algorithms. The author’s text [52] is directed toward multidimensional applications, especially the multidimensional FFT, and places the data reindexing required for several multidimensional FFT algorithms within the tensor product format.
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© 1998 Birkhäuser Boston
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Tolimieri, R., An, M. (1998). Implementation. In: Time-Frequency Representations. Applied and Numerical Harmonic Analysis. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-4152-2_15
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DOI: https://doi.org/10.1007/978-1-4612-4152-2_15
Publisher Name: Birkhäuser Boston
Print ISBN: 978-1-4612-8676-9
Online ISBN: 978-1-4612-4152-2
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