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Fast Fourier Transform for Solution of Convolution Equations on Dihedral Groups. P. 97–107
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Section: Physics. Mathematics. Informatics
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(pdf, 4.7MB )
UDC
517.9
Authors
Deundyak Vladimir Mikhaylovich,
Institute of Mathematics, Mechanics and Computer Science named after I.I. Vorovich, Southern Federal University (Rostov-on-Don, Russia)
e-mail: vlade@math.rsu.ru
Leonov Dmitriy Aleksandrovich,
Institute of Mathematics, Mechanics and Computer Science named after I.I. Vorovich, Southern Federal University (Rostov-on-Don, Russia)
e-mail: tori_92@inbox.ru
Abstract
Keywords
dihedral group, convolution equations, Fourier method, fast Fourier transform
References
- Cooley J.W., Tukey J.W. An Algorithm for Machine Calculation of Complex Fourier Series. Mathematics of Computation, 1965, vol. 19, no. 90, pp. 297–301.
- Willsky A. On the Algebraic Structure of Certain Partially Observable Finite-State Markov Processes. Information and Control, 1978, vol. 38, pp. 179–212.
- Beth T. On the Computational Complexity of the General Discrete Fourier Transform. Theor. Comp. Sci., 1987, vol. 51, pp. 331–339.
- Clausen M. Fast Generalized Fourier Transforms. Theor. Comp. Sci., 1989, vol. 67, no. 1, pp. 55–63.
- Diaconis P., Rockmore D. Efficient Computation of Fourier Inversion for Finite Groups. J. of the ACM, 1994, vol. 41, no. 1, pp. 31–66.
- Baum U. Existence and Efficient Construction of Fast Fourier Transforms for Supersolvable Groups. Computational Complexity, 1991, vol. 1, pp. 235–256.
- Brigham E. The Fast Fourier Transform and its Applications. NJ, USA, 1988.
- Diaconis P. Group Representations in Probability and Statistics. Hayward, USA, 1988.
- Lafferty J., Rockmore D. Codes and Iterative Decoding on Algebraic Expander Graphs. Proceedings of International Symposium on Information Theory and its Application, Honolulu, November 5–8, 2000. Honolulu, Hawaii, USA, 2000.
- Rockmore D. Recent Progress and Applications in Group FFTs. Computational Noncommutative Algebra and Applications, 2004, vol. 136, pp. 227–254.
- Leinz R. Using Representations of the Dihedral Groups in the Design of Early Vision Filters. Kyoto, 1993.
- Zagorodnov I.A., Tarasov R.P. Zadacha difraktsii na telakh s nekommutativnoy konechnoy gruppoy simmetriy i chislennoe ee reshenie [The Problem of Diffraction on Bodies with Non-Commutative Finite Group of Symmetries and Numerical Solution]. Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 1997, vol. 37, no. 10, pp. 1246–1262.
- Glazman I.M., Lyubich Yu.I. Konechnomernyy lineynyy analiz v zadachakh [Finite-Dimensional Linear Analysis in the Problems]. Moscow, 1969.
- Kirillov A.A. Elementy teorii predstavleniy [Elements of Theory of Representations]. Moscow, 1978.
- Hewitt E., Ross K. Abstract Harmonic Analysis. Vol. 2. Heidelberg, 1970.
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