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Volumn 26, Issue 4, 1997, Pages 1066-1099

Fast discrete polynomial transforms with applications to data analysis for distance transitive graphs

Author keywords

Discrete polynomial transform; Distance transitive graph; Fast Fourier transform; FFT; Orthogonal polynomials; Three term recurrence

Indexed keywords

DATA REDUCTION; FAST FOURIER TRANSFORMS; GRAPH THEORY; POLYNOMIALS; SET THEORY; SPECTRUM ANALYSIS; VECTORS;

EID: 0031209710     PISSN: 00975397     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0097539792240121     Document Type: Article
Times cited : (79)

References (33)
  • 2
    • 5244280077 scopus 로고
    • Representation Theory and ANOVA
    • Department of Mathematics, Harvard University, Cambridge, MA
    • R. BAILEY, P. DIACONIS, D. ROCKMORE, AND C. ROWLEY, Representation Theory and ANOVA, Technical Report, Department of Mathematics, Harvard University, Cambridge, MA, 1994.
    • (1994) Technical Report
    • Bailey, R.1    Diaconis, P.2    Rockmore, D.3    Rowley, C.4
  • 3
    • 0040455592 scopus 로고
    • Algebraic Graph Theory
    • Cambridge University Press, Cambridge, UK
    • N. BIGGS, Algebraic Graph Theory, Cambridge Tracts in Mathematics 67, Cambridge University Press, Cambridge, UK, 1974.
    • (1974) Cambridge Tracts in Mathematics , vol.67
    • Biggs, N.1
  • 6
    • 0040170055 scopus 로고
    • Addition requirements for matrix and transposed matrix products
    • N. BSHOUTY, M. KAMINSKI, AND D. KIRKPATRICK, Addition requirements for matrix and transposed matrix products, J. Algorithms, 9 (1988), pp. 354-364.
    • (1988) J. Algorithms , vol.9 , pp. 354-364
    • Bshouty, N.1    Kaminski, M.2    Kirkpatrick, D.3
  • 9
    • 0039578698 scopus 로고
    • Efficient computation of isotropic projections for the symmetric group
    • L. Finkelstein and W. Kantor, eds., AMS, Providence, RI
    • P. DIACONIS AND D. ROCKMORE, Efficient computation of isotropic projections for the symmetric group, in DIMACS Series in Discrete Mathematics and Theoretical Computer Science, Vol. 11, L. Finkelstein and W. Kantor, eds., AMS, Providence, RI, 1992, pp. 87-104.
    • (1992) DIMACS Series in Discrete Mathematics and Theoretical Computer Science , vol.11 , pp. 87-104
    • Diaconis, P.1    Rockmore, D.2
  • 10
    • 0000273884 scopus 로고
    • Computing Fourier transforms and convolutions on the 2-sphere
    • J. R. DRISCOLL AND D. HEALY, Computing Fourier transforms and convolutions on the 2-sphere, Adv. Appl. Math., 15 (1994), pp. 202-250.
    • (1994) Adv. Appl. Math. , vol.15 , pp. 202-250
    • Driscoll, J.R.1    Healy, D.2
  • 12
    • 84966204289 scopus 로고
    • On the construction of Gaussian quadrature rules from modified moments
    • W. GAUTSCHI, On the construction of Gaussian quadrature rules from modified moments, Math. Comp., 24 (1970), pp. 245-260.
    • (1970) Math. Comp. , vol.24 , pp. 245-260
    • Gautschi, W.1
  • 13
    • 0012411229 scopus 로고
    • Questions of numerical condition related to polynomials
    • G. Golub, ed., MAA, Washington, DC
    • W. GAUTSCHI, Questions of numerical condition related to polynomials, in Studies in Numerical Analysis, G. Golub, ed., MAA, Washington, DC, 1984, pp. 140-177.
    • (1984) Studies in Numerical Analysis , pp. 140-177
    • Gautschi, W.1
  • 14
    • 84967713478 scopus 로고
    • Some applications of Gelfand pairs to number theory
    • B. GROSS, Some applications of Gelfand pairs to number theory, Bull. Amer. Math. Soc., 24 (1991), pp. 277-301.
    • (1991) Bull. Amer. Math. Soc. , vol.24 , pp. 277-301
    • Gross, B.1
  • 15
    • 85033168519 scopus 로고
    • Efficiency and Stability Issues in the Numerical Computation of Fourier Transforms on the 2-Sphere
    • Department of Mathematics and Computer Science, Dartmouth College, Hanover, NH
    • D. HEALY, S. MOORE, AND D. ROCKMORE, Efficiency and Stability Issues in the Numerical Computation of Fourier Transforms on the 2-Sphere, Technical Report PCS-TR94-222, Department of Mathematics and Computer Science, Dartmouth College, Hanover, NH, 1993.
    • (1993) Technical Report PCS-TR94-222
    • Healy, D.1    Moore, S.2    Rockmore, D.3
  • 18
    • 0012063613 scopus 로고
    • Fast solution of Vandermonde-like systems involving orthogonal polynomials
    • N. J. HIGHAM, Fast solution of Vandermonde-like systems involving orthogonal polynomials, IMA J. Numer. Anal., 8 (1988), pp. 473-486.
    • (1988) IMA J. Numer. Anal. , vol.8 , pp. 473-486
    • Higham, N.J.1
  • 19
    • 0003082366 scopus 로고
    • The Hahn polynomials, formulas and an application
    • S. KARLIN AND J. L. MCGREGOR, The Hahn polynomials, formulas and an application, Scripta Math., 26 (1961), pp. 33-46.
    • (1961) Scripta Math. , vol.26 , pp. 33-46
    • Karlin, S.1    Mcgregor, J.L.2
  • 20
    • 0038929679 scopus 로고
    • Ph.D. thesis, Department of Mathematics, Harvard University, Cambridge, MA
    • D. MASLEN, Fast Transforms and Sampling for Compact Groups, Ph.D. thesis, Department of Mathematics, Harvard University, Cambridge, MA, 1993.
    • (1993) Fast Transforms and Sampling for Compact Groups
    • Maslen, D.1
  • 21
    • 21144466359 scopus 로고
    • Symmetry stabilization for polynomial evaluation and interpolation
    • S. MOORE, D. HEALY, AND D. ROCKMORE, Symmetry stabilization for polynomial evaluation and interpolation, Linear Algebra Appl., 192 (1993), pp. 249-299.
    • (1993) Linear Algebra Appl. , vol.192 , pp. 249-299
    • Moore, S.1    Healy, D.2    Rockmore, D.3
  • 25
    • 0026870395 scopus 로고
    • Matrix and polynomial computations
    • V. PAN, Matrix and polynomial computations, SIAM Review, 34 (1992), pp. 225-262.
    • (1992) SIAM Review , vol.34 , pp. 225-262
    • Pan, V.1
  • 27
    • 0011415426 scopus 로고
    • Orthogonal polynomials and Chevalley groups
    • R. Askey, T. Koornwinder, and W. Schempp, eds., Reidel, Dordrecht, The Netherlands
    • D. STANTON, Orthogonal polynomials and Chevalley groups, in Special Functions: Group Theoretical Aspects and Applications, R. Askey, T. Koornwinder, and W. Schempp, eds., Reidel, Dordrecht, The Netherlands, 1984, pp. 87-128.
    • (1984) Special Functions: Group Theoretical Aspects and Applications , pp. 87-128
    • Stanton, D.1
  • 28
  • 29
    • 0011414687 scopus 로고
    • An introduction to group representations and orthogonal polynomials
    • P. Nevai, ed., Kluwer Academic Publishers, Norwell, MA
    • D. STANTON, An introduction to group representations and orthogonal polynomials, in Orthogonal Polynomials, P. Nevai, ed., Kluwer Academic Publishers, Norwell, MA, 1990, pp. 419-433.
    • (1990) Orthogonal Polynomials , pp. 419-433
    • Stanton, D.1
  • 30
    • 0026267116 scopus 로고
    • On scalar and vector transform methods for global spectral models
    • C. TEMPERTON, On scalar and vector transform methods for global spectral models, Monthly Weather Review, 119 (1991), pp. 1303-1307.
    • (1991) Monthly Weather Review , vol.119 , pp. 1303-1307
    • Temperton, C.1
  • 32
    • 0040577622 scopus 로고
    • Spherical functions on finite groups
    • D. TRAVIS, Spherical functions on finite groups, J. Algebra, 29 (1974), pp. 65-76.
    • (1974) J. Algebra , vol.29 , pp. 65-76
    • Travis, D.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.