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Volumn 67, Issue 224, 1998, Pages 1577-1590

Fast algorithms for discrete polynomial transforms

Author keywords

Cascade summation; Chebyshev knots; Discrete polynomial transform; Fast cosine transform; Fast polynomial transform; Vandermonde like matrix

Indexed keywords


EID: 0032367851     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0025-5718-98-00975-2     Document Type: Article
Times cited : (81)

References (20)
  • 1
    • 0000944835 scopus 로고
    • A fast algorithm for the evaluation of Legendre expansions
    • MR 91i:65042
    • B. K. Alpert and V. Rokhlin, A fast algorithm for the evaluation of Legendre expansions, SIAM J. Sci. Statist. Comput. 12 (1991), 158 - 179. MR 91i:65042
    • (1991) SIAM J. Sci. Statist. Comput. , vol.12 , pp. 158-179
    • Alpert, B.K.1    Rokhlin, V.2
  • 2
    • 0040844860 scopus 로고    scopus 로고
    • Fast polynomial multiplication and convolutions related to the discrete cosine transform
    • CMP 97:06
    • G. Baszenski and M. Tasche, Fast polynomial multiplication and convolutions related to the discrete cosine transform, Linear Algebra Appl. 252 (1997), 1 - 25. CMP 97:06
    • (1997) Linear Algebra Appl. , vol.252 , pp. 1-25
    • Baszenski, G.1    Tasche, M.2
  • 3
    • 0001601097 scopus 로고
    • On the associated orthogonal polynomials
    • MR 92e:33007
    • S. Belmehdi, On the associated orthogonal polynomials, J. Comput. Appl. Math. 32 (1991), 311 - 319. MR 92e:33007
    • (1991) J. Comput. Appl. Math. , vol.32 , pp. 311-319
    • Belmehdi, S.1
  • 5
    • 84968505704 scopus 로고
    • A note on the summation of Chebyshev series
    • MR 17:194e
    • C. W. Clenshaw, A note on the summation of Chebyshev series. Math. Comp. 9 (1955), 118 - 120. MR 17:194e
    • (1955) Math. Comp. , vol.9 , pp. 118-120
    • Clenshaw, C.W.1
  • 6
    • 0000273884 scopus 로고
    • Computing fourier transforms and convolutions on the 2-sphere
    • MR 95h:65108
    • J. R. Driscoll and D.M. Healy, Computing Fourier transforms and convolutions on the 2-sphere, Adv. in Appl. Math. 15 (1994), 202 - 240. MR 95h:65108
    • (1994) Adv. in Appl. Math. , vol.15 , pp. 202-240
    • Driscoll, J.R.1    Healy, D.M.2
  • 7
    • 0031209710 scopus 로고    scopus 로고
    • Fast discrete polynomial transforms with applications to data analysis for distance transitive graphs
    • CMP 97:15
    • J. R. Driscoll, D. M. Healy and D. Rockmore, Fast discrete polynomial transforms with applications to data analysis for distance transitive graphs, SIAM J. Sci. Comput. 26 (1997), 1066-1099. CMP 97:15
    • (1997) SIAM J. Sci. Comput. , vol.26 , pp. 1066-1099
    • Driscoll, J.R.1    Healy, D.M.2    Rockmore, D.3
  • 8
    • 0009902928 scopus 로고    scopus 로고
    • Fast algorithms for polynomial interpolation, integration and differentiation
    • MR 97h:65015
    • A. Dutt, M. Gu and V. Rokhlin, Fast algorithms for polynomial interpolation, integration and differentiation, SIAM J. Numer. Anal. 33 (1996), 1689-1711. MR 97h:65015
    • (1996) SIAM J. Numer. Anal. , vol.33 , pp. 1689-1711
    • Dutt, A.1    Gu, M.2    Rokhlin, V.3
  • 9
    • 0001415134 scopus 로고
    • The condition of Vandermonde-like matrices involving orthogonal polynomials
    • MR 84i:65043
    • W. Gautschi, The condition of Vandermonde-like matrices involving orthogonal polynomials, Linear Algebra Appl. 52/53 (1983), 293 - 300. MR 84i:65043
    • (1983) Linear Algebra Appl. , vol.52-53 , pp. 293-300
    • Gautschi, W.1
  • 11
    • 0012063613 scopus 로고
    • Fast solution of vandermonde-like systems involving orthogonal polynomials
    • MR 89k:65067
    • N. J. Higham, Fast solution of Vandermonde-like systems involving orthogonal polynomials, IMA J. Numer. Anal. 8 (1988), 473 - 486. MR 89k:65067
    • (1988) IMA J. Numer. Anal. , vol.8 , pp. 473-486
    • Higham, N.J.1
  • 13
    • 0040223415 scopus 로고
    • Efficient stabilization methods for fast polynomial transforms, thesis
    • S. S. B. Moore, Efficient stabilization methods for fast polynomial transforms, Thesis, Dartmouth College, 1994.
    • (1994) Dartmouth College
    • Moore, S.S.B.1
  • 14
    • 21144466359 scopus 로고
    • Symmetry stabilization for fast discrete monomial transforms and polynomial evaluation
    • MR 94g:65148
    • S. S. B. Moore, D.M. Healy and D.N. Rockmore, Symmetry stabilization for fast discrete monomial transforms and polynomial evaluation, Linear Algebra Appl. 192 (1993), 249 -299. MR 94g:65148
    • (1993) Linear Algebra Appl. , vol.192 , pp. 249-299
    • Moore, S.S.B.1    Healy, D.M.2    Rockmore, D.N.3
  • 15
    • 0039631438 scopus 로고
    • Fast eigenfunction transforms
    • G.C. Rota, ed., Academic Press, New York
    • S. A. Orszag, Fast eigenfunction transforms, in: Science and Computers (G.C. Rota, ed.), Academic Press, New York, 1986, 23 - 30.
    • (1986) Science and Computers , pp. 23-30
    • Orszag, S.A.1
  • 16
    • 0001116810 scopus 로고
    • Fast evaluation and interpolation at the Chebyshev sets of points
    • CMP 21:17
    • V. Pan, Fast evaluation and interpolation at the Chebyshev sets of points, Appl. Math. Lett. 34 (1989), 255 - 258. CMP 21:17
    • (1989) Appl. Math. Lett. , vol.34 , pp. 255-258
    • Pan, V.1
  • 18
    • 0039928421 scopus 로고
    • Fast radix-p discrete cosine transform
    • MR 95m:65221
    • G. Steidl, Fast radix-p discrete cosine transform, Appl. Algebra, in Engrg. Comm. Comput. 3 (1992), 39 - 46. MR 95m:65221
    • (1992) Appl. Algebra, in Engrg. Comm. Comput. , vol.3 , pp. 39-46
    • Steidl, G.1
  • 19
    • 84966222128 scopus 로고
    • A polynomial approach to fast algorithms for discrete fourier-cosine and fourier-sine transforms
    • MR 91h:65225
    • G. Steidl and M. Tasche, A polynomial approach to fast algorithms for discrete Fourier-cosine and Fourier-sine transforms, Math. Comp. 56 (1991), 281 - 296. MR 91h:65225
    • (1991) Math. Comp. , vol.56 , pp. 281-296
    • Steidl, G.1    Tasche, M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.