The future fast fourier transform?

SIAM Journal on Scientific Computing

Volumn 20, Issue 3, 1998, Pages 1094-1114

  Edelman, Alan ^a,b,c   McCorquodale, Peter ^a,b   Toledo, Sivan ^a,c  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^b LAWRENCE BERKELEY NATIONAL LABORATORY   (United States)

^c PALO ALTO RESEARCH CENTER   (United States)

Author keywords

Fast multipole method; Parallel fourier transforms

Indexed keywords

FAST MULTIPOLE METHOD; PARALLEL FOURIER TRANSFORMS;

ALGORITHMS; BANDWIDTH; MATRIX ALGEBRA; PARALLEL PROCESSING SYSTEMS; VECTORS;

FAST FOURIER TRANSFORMS;

EID: 0032226441     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1064827597316266     Document Type: Article

References (23)

1. R. C. AGARWAL, F. G. GUSTAVSON, AND M. ZUBAIR, Exploiting functional parallelism of POWER'2 to design high-performance numerical algorithms, IBM Journal of Research and Development, 38 (1994), pp. 563-576.
2. T. AGERWALA, J. L. MARTIN, J. H. MIRZA, D. C. SADLER, D. M. DIAS, AND M. SNIR, SP2 system architecture, IBM Systems Journal, 34 (1995) pp. 152-184.
3. H. C. ANDREWS AND C. L. PATTERSON, Singular value decomposition (SVD) image coding, IEEE Trans. Commun., COM-24 (1976) pp. 425-432.
4. D. H. BAILEY, FFTs in external or hierarchical memory, J. Supercomput., 4 (1990), pp. 23-35.
5. E. G. BENSON, D. C. P. LAFRANCE-LINDEN, R. A. WARREN, AND S. WIRYAMAN, Design of digital's parallel software environment, Digital Technical Journal, 7 (1995), pp. 24-38.
6. W. T. COCHRANE, J. W. COOLEY, J. W. FAVIX, D. L. HELMS, R. A. KAENEL, W. W. LANG, G. C. MALIXG, D. E. NELSON, C. M. RADER, AND P. D. WELCH, \Vhat is the fast Fourier transform? IEEE Trans. Audio and Electroacoustics, AU-15 (19G7), pp. 45-55.
7. J. W. COOLEY AND J. W. TUKEY, An algorithm for the machine calculation of complex Fourier series, Math. Comput., 19 (19G5), pp. 297-301.
8. T. H. CORMEN AND D. M. NlCOL, Performing Out-of-Core FFTs on Parallel Disk Systems, Technical Report PCS-TR96-294, Dartmouth College, Hanover, NH, 1996.
9. A. DUTT, M. Gu, AND V. ROKIILIN, Fast Algorithms for Polynomial Interpolation, Integration and Differentiation, Research Report YALEU/DCS/RR-977, Yale University, New Haven, CT, 1993.
10. A. DUTT AND V. ROKHLIN, Fast Fourier transforms for nonequispaccd data, II, Appl. Comput. Harmon. Anal., 2 (1995), pp. 85-100.
11. G. H. GOLUB AND C. F. VAN LOAN, Matrix Computations, 2nd ed., The Johns Hopkins University Press, Baltimore, London, 1989.
12. L. GREENGARD AND W. D. GROPP, A parallel version of the fast multipole method, Comput. Math. Applic., 20 (1990), pp. G3-71.
13. U. GRENANDER AND G. SZEGö, Toeplitz Forms and Their Applications, University of California Press, Berkeley, Los Angeles, 1958.
14. F. A. GRÜNBAUM, Eigenvectors of a Toeplitz matrix: discrete version of the prolate spheroidal wave functions, SIAM J. Alg. Discrete Methods, 2 (1981), pp. 13G-141.
15. S. K. S. GUPTA, C.-H. HUANG, P. SADAYAPPAN, AND R. W. JOHNSON, Implementing fast Fourier transforms on distributed-memory multiprocessors using data redistributions, Parallel Process. Lett., 4 (1994), pp. 477-488.
16. J. KATZENELSON, Computational structure of the N-body problem, SIAM J. Sei. Statist. Cornput., 10 (1989), pp. 787-815.
17. D. SLEPIAN, Prolate spheroidal wave functions, Fourier analysis, and uncertainty V: the discrete case, Bell System Tech. J., 57 (1978), pp. 1371-1430.
18. P. N. SWARZTRAUBER, Multiprocessor FFTs, Parallel Comput., 5 (1987) pp. 197-210.
19. P. N. SWARZTRAUBER, Vectorizing the FFT, in Parallel Computations, G. Rodrigue, éd., Academic Press, New York, 1982, pp. 51-83.
20. C. F. VAN LOAN, Computational Frameworks for the Fast Fourier Transform, SIAM, Philadelphia, 1992.
21. J. M. VARAH, The prolate matrix, Linear Algebra Appl., 187 (1993), pp. 269-278.
22. S. W. WHITE AND S. DIIAWAN, POWER1: next generation of the RISC System/6000 family, IBM Journal of Research and Development, 38 (1994), pp. 493-502.
23. P. MCCORQUODALE, Fast Multipole-Type Methods in One and Two Dimensions, with Application to Parallel Fourier Transforms, Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, MA, 1998.