메뉴 건너뛰기




Volumn 24, Issue 6, 2003, Pages 2013-2037

Fast summation at nonequispaced knots by NFFTs

Author keywords

Fast discrete summation; Fast Fourier transform at nonequispaced knots; Radial basis functions; Toeplitz matrices

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; DIGITAL ARITHMETIC; INTEGRAL EQUATIONS; MATRIX ALGEBRA; PARTIAL DIFFERENTIAL EQUATIONS;

EID: 0348207634     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1064827502400984     Document Type: Article
Times cited : (80)

References (34)
  • 1
    • 0000139676 scopus 로고
    • Wavelet-like bases for the fast solution of second-kind integral equations
    • B. Alpert, G. Beylkin, R. Cofiman, and V. Rokhlin, Wavelet-like bases for the fast solution of second-kind integral equations, SIAM J. Sci. Comput., 14 (1993), pp. 159-184.
    • (1993) SIAM J. Sci. Comput. , vol.14 , pp. 159-184
    • Alpert, B.1    Beylkin, G.2    Cofiman, R.3    Rokhlin, V.4
  • 2
    • 0000989499 scopus 로고
    • A method of local corrections for computing the velocity field due to a distribution of vortex blobs
    • C. Anderson, A method of local corrections for computing the velocity field due to a distribution of vortex blobs, J. Comput. Phys., 62 (1986), pp. 111-123.
    • (1986) J. Comput. Phys. , vol.62 , pp. 111-123
    • Anderson, C.1
  • 3
    • 0001922098 scopus 로고    scopus 로고
    • A short course on fast multipole methods
    • M. Ainsworth, J. Levesley, W. A. Light, and M. Marletta, eds., Clarendon Press, Oxford, UK
    • R. K. Beatson and L. Greengard, A short course on fast multipole methods, in Wavelets, Multilevel Methods and Elliptic PDEs, M. Ainsworth, J. Levesley, W. A. Light, and M. Marletta, eds., Clarendon Press, Oxford, UK, 1997.
    • (1997) Wavelets, Multilevel Methods and Elliptic PDEs
    • Beatson, R.K.1    Greengard, L.2
  • 4
    • 0031488175 scopus 로고    scopus 로고
    • Fast evaluation of radial basis functions: Methods for 2-dimensional polyharmonic splines
    • R. K. Beatson and W. A. Light, Fast evaluation of radial basis functions: Methods for 2-dimensional polyharmonic splines, IMA J. Numer. Anal., 17 (1997). pp. 343-372.
    • (1997) IMA J. Numer. Anal. , vol.17 , pp. 343-372
    • Beatson, R.K.1    Light, W.A.2
  • 5
    • 0003024724 scopus 로고
    • Fast evaluation of radial basis functions: I
    • R. K. Beatson and G. N. Newsam, Fast evaluation of radial basis functions: I., Comput. Math. Appl., 24 (1992), pp. 7-19.
    • (1992) Comput. Math. Appl. , vol.24 , pp. 7-19
    • Beatson, R.K.1    Newsam, G.N.2
  • 6
    • 3142776518 scopus 로고
    • On the fast Fourier transform of functions with singularities
    • G. Beylkin, On the fast Fourier transform of functions with singularities, Appl. Comput. Harmon. Anal., 2 (1995), pp. 363-381.
    • (1995) Appl. Comput. Harmon. Anal. , vol.2 , pp. 363-381
    • Beylkin, G.1
  • 7
    • 84990610636 scopus 로고
    • Fast wavelet transforms and numerical algorithms I
    • G. Beylkin, R. Coifman, and V. Rokhlin, Fast wavelet transforms and numerical algorithms I, Comm. Pure Appl. Math., 44 (1991), pp. 141-183.
    • (1991) Comm. Pure Appl. Math. , vol.44 , pp. 141-183
    • Beylkin, G.1    Coifman, R.2    Rokhlin, V.3
  • 8
    • 0037250788 scopus 로고    scopus 로고
    • A multiresolution approach to regularization of singular operators and fast summation
    • G. Beylkin and R. Cramer, A multiresolution approach to regularization of singular operators and fast summation, SIAM J. Sci. Comput., 24 (2002), pp. 81-117.
    • (2002) SIAM J. Sci. Comput. , vol.24 , pp. 81-117
    • Beylkin, G.1    Cramer, R.2
  • 9
    • 0036449856 scopus 로고    scopus 로고
    • A fast solver for Fredholm equations of the second kind with weakly singular kernels
    • R. H. Chan, F. R. Lin, and C. F. Chan, A fast solver for Fredholm equations of the second kind with weakly singular kernels, J. Numer. Math., 10 (2002), pp. 13-36.
    • (2002) J. Numer. Math. , vol.10 , pp. 13-36
    • Chan, R.H.1    Lin, F.R.2    Chan, C.F.3
  • 10
    • 0030246195 scopus 로고    scopus 로고
    • Conjugate gradient methods of Toeplitz systems
    • R. H. Chan and M. K. Ng, Conjugate gradient methods of Toeplitz systems, SIAM Rev., 38 (1996), pp. 427-482.
    • (1996) SIAM Rev. , vol.38 , pp. 427-482
    • Chan, R.H.1    Ng, M.K.2
  • 11
    • 0033102416 scopus 로고    scopus 로고
    • Nonuniform fast Fourier transform
    • A. J. W. Duijndam and M. A. Schonewille, Nonuniform fast Fourier transform, Geophysics, 64 (1999), pp. 539-551.
    • (1999) Geophysics , vol.64 , pp. 539-551
    • Duijndam, A.J.W.1    Schonewille, M.A.2
  • 12
    • 0009902928 scopus 로고    scopus 로고
    • Fast algorithms for polynomial interpolation, integration, and differentiation
    • A. Dutt, M. Gu, and V. Rokhlin, Fast algorithms for polynomial interpolation, integration, and differentiation, SIAM J. Numer. Anal., 33 (1996), pp. 1689-1711.
    • (1996) SIAM J. Numer. Anal. , vol.33 , pp. 1689-1711
    • Dutt, A.1    Gu, M.2    Rokhlin, V.3
  • 13
    • 0000527817 scopus 로고
    • Fast Fourier transforms for nonequispaced data
    • A. Dutt and V. Rokhlin, Fast Fourier transforms for nonequispaced data, SIAM J. Sci. Comput., 14 (1993), pp. 1368-1393.
    • (1993) SIAM J. Sci. Comput. , vol.14 , pp. 1368-1393
    • Dutt, A.1    Rokhlin, V.2
  • 14
    • 85160587383 scopus 로고    scopus 로고
    • Nonuniform fast Fourier transforms using min-max interpolation
    • to appear
    • J. A. Fessler and B. P. Sutton, Nonuniform fast Fourier transforms using min-max interpolation, IEEE Trans. Signal Process., to appear.
    • IEEE Trans. Signal Process.
    • Fessler, J.A.1    Sutton, B.P.2
  • 15
    • 0003791802 scopus 로고    scopus 로고
    • Schnelle Fourier-Transformation bei nichtäquidistanten Gittern und tomographische Anwendungen
    • Dissertation, Universität Münster, Münster, Germany
    • K. Fourmont, Schnelle Fourier-Transformation bei nichtäquidistanten Gittern und tomographische Anwendungen, Dissertation, Universität Münster, Münster, Germany, 1999.
    • (1999)
    • Fourmont, K.1
  • 18
    • 0000396658 scopus 로고
    • A fast algorithm for particle simulations
    • L. Greengard and V. Rokhlin, A fast algorithm for particle simulations, J. Comput. Phys., 73 (1987), pp. 325-348.
    • (1987) J. Comput. Phys. , vol.73 , pp. 325-348
    • Greengard, L.1    Rokhlin, V.2
  • 19
    • 0032637646 scopus 로고    scopus 로고
    • A sparse matrix arithmetic based on H-matrices, Part I: Introduction to H-matrices
    • W. Hackbusch, A sparse matrix arithmetic based on H-matrices, Part I: Introduction to H-matrices, Computing, 62, (1999), pp. 89-108.
    • (1999) Computing , vol.62 , pp. 89-108
    • Hackbusch, W.1
  • 20
    • 0001617415 scopus 로고
    • On the fast matrix multiplication in the boundary element method by panel clustering
    • W. Hackbusch and Z. P. Nowak, On the fast matrix multiplication in the boundary element method by panel clustering, Numer. Math., 54 (1989), pp. 463-491.
    • (1989) Numer. Math. , vol.54 , pp. 463-491
    • Hackbusch, W.1    Nowak, Z.P.2
  • 21
    • 0028485163 scopus 로고
    • Fast multiresolution algorithms for matrix-vector multiplication
    • A. Harten and I. Yad-Shalom, Fast multiresolution algorithms for matrix-vector multiplication, SIAM J. Numer. Anal., 31 (1994), pp. 1191-1218.
    • (1994) SIAM J. Numer. Anal. , vol.31 , pp. 1191-1218
    • Harten, A.1    Yad-Shalom, I.2
  • 22
    • 0026219520 scopus 로고
    • Selection of a convolution function for Fourier inversion using gridding
    • J. I. Jackson, Selection of a convolution function for Fourier inversion using gridding, IEEE Trans. Med. Imag., 10 (1991), pp. 473-478.
    • (1991) IEEE Trans. Med. Imag. , vol.10 , pp. 473-478
    • Jackson, J.I.1
  • 23
    • 85160612341 scopus 로고
    • Matrix sparsification by discrete multiscale methods
    • C. K. Chui and L. L. Schumaker, eds., World Scientific, River Edge, NJ
    • M. Konik, R. Schneider, and G. Steidl, Matrix sparsification by discrete multiscale methods, in Approximation Theory VIII: Approximation and Decomposition, C. K. Chui and L. L. Schumaker, eds., World Scientific, River Edge, NJ, 1995.
    • (1995) Approximation Theory VIII: Approximation and Decomposition
    • Konik, M.1    Schneider, R.2    Steidl, G.3
  • 24
    • 0242659618 scopus 로고    scopus 로고
    • NFFT, softwarepackage, C subroutine library
    • S. Kunis and D. Potts, NFFT, Softwarepackage, C subroutine library, http://www.math.uni-luebeck.de/potts/nfft (2002).
    • (2002)
    • Kunis, S.1    Potts, D.2
  • 25
    • 0033295052 scopus 로고    scopus 로고
    • The regular Fourier matrices and nonuniform fast Fourier transforms
    • N. Nguyen and Q. H. Liu, The regular Fourier matrices and nonuniform fast Fourier transforms, SIAM J. Sci. Comput., 21 (1999), pp. 283-293.
    • (1999) SIAM J. Sci. Comput. , vol.21 , pp. 283-293
    • Nguyen, N.1    Liu, Q.H.2
  • 26
    • 85160635683 scopus 로고    scopus 로고
    • Approximate factorizations of Fourier matrices with nonequispaced knots
    • to appear
    • A. Nieslony and G. Steidl, Approximate factorizations of Fourier matrices with nonequispaced knots, Linear Algebra Appl., to appear.
    • Linear Algebra Appl.
    • Nieslony, A.1    Steidl, G.2
  • 27
    • 0041876673 scopus 로고    scopus 로고
    • Optimal trigonometric preconditioners for nonsymmetric Toeplitz systems
    • D. Potts and G. Steidl, Optimal trigonometric preconditioners for nonsymmetric Toeplitz systems, Linear Algebra Appl., 281 (1998), pp. 265-292.
    • (1998) Linear Algebra Appl. , vol.281 , pp. 265-292
    • Potts, D.1    Steidl, G.2
  • 28
    • 0002895445 scopus 로고    scopus 로고
    • Trigonometric preconditioners for block Toeplitz systems
    • G. Nürnberger, J. W. Schmidt, and G. Walz, eds., Birkhäuser, Basel
    • D. Potts, G. Steidl, and M. Tasche, Trigonometric preconditioners for block Toeplitz systems, in Multivariate Approximation and Splines, G. Nürnberger, J. W. Schmidt, and G. Walz, eds., Birkhäuser, Basel, 1997, pp. 219-234.
    • (1997) Multivariate Approximation and Splines , pp. 219-234
    • Potts, D.1    Steidl, G.2    Tasche, M.3
  • 29
    • 0011937243 scopus 로고    scopus 로고
    • Fast Fourier transforms for nonequispaced data: A tutorial
    • J. J. Benedetto and P. J. S. G. Ferreira, eds., Birkhäser, Boston
    • D. Potts, G. Steidl, and M. Tasche, Fast Fourier transforms for nonequispaced data: A tutorial, in Modern Sampling Theory: Mathematics and Applications, J. J. Benedetto and P. J. S. G. Ferreira, eds., Birkhäser, Boston, 2001, pp. 247-270.
    • (2001) Modern Sampling Theory: Mathematics and Applications , pp. 247-270
    • Potts, D.1    Steidl, G.2    Tasche, M.3
  • 31
    • 22444454428 scopus 로고    scopus 로고
    • A note on fast Fourier transforms for nonequispaced grids
    • G. Steidl, A note on fast Fourier transforms for nonequispaced grids, Adv. Comput. Math., 9 (1998), pp. 337-353.
    • (1998) Adv. Comput. Math. , vol.9 , pp. 337-353
    • Steidl, G.1
  • 32
    • 0035359436 scopus 로고    scopus 로고
    • A matrix version of the fast multipole method
    • X. Sun and N. P. Pitsianis, A matrix version of the fast multipole method, SIAM Rev., 43 (2001), pp. 289-300.
    • (2001) SIAM Rev. , vol.43 , pp. 289-300
    • Sun, X.1    Pitsianis, N.P.2
  • 33
    • 0029692981 scopus 로고    scopus 로고
    • Mosaic-skeleton approximations
    • E. E. Tyrtyshnikov, Mosaic-skeleton approximations, Calcolo, 33 (1996), pp. 47-57.
    • (1996) Calcolo , vol.33 , pp. 47-57
    • Tyrtyshnikov, E.E.1
  • 34
    • 0005931337 scopus 로고    scopus 로고
    • An improved fast multipole algorithm for potential fields on the line
    • N. Yarvin and V. Rokhlin, An improved fast multipole algorithm for potential fields on the line, SIAM J. Numer. Anal., 36 (1999), pp. 629-666.
    • (1999) SIAM J. Numer. Anal. , vol.36 , pp. 629-666
    • Yarvin, N.1    Rokhlin, V.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.