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Volumn 26, Issue 1, 2010, Pages 51-81

Fast discrete algorithms for sparse Fourier expansions of high dimensional functions

Author keywords

Fast discrete algorithm; Hyperbolic cross Fourier expansion; Sparse grid

Indexed keywords

FOURIER ANALYSIS; FOURIER OPTICS; FOURIER TRANSFORMS; INTERPOLATION; NUMERICAL METHODS; POLYNOMIAL APPROXIMATION; WAVEFORM ANALYSIS;

EID: 71649098161     PISSN: 0885064X     EISSN: 10902708     Source Type: Journal    
DOI: 10.1016/j.jco.2009.10.001     Document Type: Article
Times cited : (25)

References (40)
  • 1
    • 71649087176 scopus 로고
    • Asymptotically optimal sampling schemes for periodic functions II: The multivariate case
    • Chui C.K., Schempp W., and Zeller K. (Eds), Birkhäuser, Basel
    • Chen H., Chui C.K., and Micchelli C.A. Asymptotically optimal sampling schemes for periodic functions II: The multivariate case. In: Chui C.K., Schempp W., and Zeller K. (Eds). Multivariate Approximation Theory IV, ISNM 90 (1989), Birkhäuser, Basel 73-86
    • (1989) Multivariate Approximation Theory IV, ISNM 90 , pp. 73-86
    • Chen, H.1    Chui, C.K.2    Micchelli, C.A.3
  • 2
    • 0034337983 scopus 로고    scopus 로고
    • Optimized tensor-product approximation spaces
    • Griebel M., and Knapek S. Optimized tensor-product approximation spaces. Constr. Approx. 16 (2000) 525-540
    • (2000) Constr. Approx. , vol.16 , pp. 525-540
    • Griebel, M.1    Knapek, S.2
  • 3
    • 0003303299 scopus 로고
    • Approximation of functions with bounded mixed derivative
    • Temlyakov V. Approximation of functions with bounded mixed derivative. Trudy Mat. Inst. Steklov. 178 (1986) 1-112
    • (1986) Trudy Mat. Inst. Steklov. , vol.178 , pp. 1-112
    • Temlyakov, V.1
  • 4
    • 55349121543 scopus 로고    scopus 로고
    • A fast Fourier-Galerkin method for solving singular boundary integral equations
    • Cai H., and Xu Y. A fast Fourier-Galerkin method for solving singular boundary integral equations. SIAM J. Numer. Anal. 46 (2008) 1965-1984
    • (2008) SIAM J. Numer. Anal. , vol.46 , pp. 1965-1984
    • Cai, H.1    Xu, Y.2
  • 5
    • 0030099613 scopus 로고    scopus 로고
    • Information complexity of multivariate Fredholm equations in sobolev classes
    • Frank K., Heinrich S., and Pereverzev S. Information complexity of multivariate Fredholm equations in sobolev classes. J. Complexity 12 (1996) 17-34
    • (1996) J. Complexity , vol.12 , pp. 17-34
    • Frank, K.1    Heinrich, S.2    Pereverzev, S.3
  • 6
    • 71649115133 scopus 로고    scopus 로고
    • S. Knapek, Hyperbolic cross approximation of integral operators with smooth kernel, Technical Report 665, SFB 256, Univ. Bonn, 2000
    • S. Knapek, Hyperbolic cross approximation of integral operators with smooth kernel, Technical Report 665, SFB 256, Univ. Bonn, 2000
  • 9
    • 34249925524 scopus 로고
    • Hyperbolic cross and the complexity of the approximate solution of Fredholm integral equations of the second kind with differentiable kernels
    • Pereverzev S.V. Hyperbolic cross and the complexity of the approximate solution of Fredholm integral equations of the second kind with differentiable kernels. Siberian Math. J. 32 (1991) 85-92
    • (1991) Siberian Math. J. , vol.32 , pp. 85-92
    • Pereverzev, S.V.1
  • 10
    • 0343056203 scopus 로고
    • A discrete Fourier transform scheme for Boolean sums of trigonometric operators
    • Chui C.K., Schempp W., and Zeller K. (Eds), Birkhäuser, Basel
    • Baszenski G., and Delvos F.J. A discrete Fourier transform scheme for Boolean sums of trigonometric operators. In: Chui C.K., Schempp W., and Zeller K. (Eds). Multivariate Approximation Theory IV, ISNM 90 (1989), Birkhäuser, Basel 15-24
    • (1989) Multivariate Approximation Theory IV, ISNM 90 , pp. 15-24
    • Baszenski, G.1    Delvos, F.J.2
  • 11
    • 21144461257 scopus 로고
    • Fourier transform on sparse grids with hierarchical bases
    • Hallatschek K. Fourier transform on sparse grids with hierarchical bases. Numer. Math. 63 (1992) 83-97
    • (1992) Numer. Math. , vol.63 , pp. 83-97
    • Hallatschek, K.1
  • 12
    • 34249087785 scopus 로고    scopus 로고
    • Fourier transform on sparse grids: Code design and the time dependent Schrödinger equation
    • Gradinaru V. Fourier transform on sparse grids: Code design and the time dependent Schrödinger equation. Computing 80 (2007) 1-22
    • (2007) Computing , vol.80 , pp. 1-22
    • Gradinaru, V.1
  • 13
    • 55549120221 scopus 로고    scopus 로고
    • Strang splitting for the time dependent Schrödinger equation on sparse grids
    • Gradinaru V. Strang splitting for the time dependent Schrödinger equation on sparse grids. SIAM J. Numer. Anal. 46 (2007) 103-123
    • (2007) SIAM J. Numer. Anal. , vol.46 , pp. 103-123
    • Gradinaru, V.1
  • 14
    • 0005054331 scopus 로고
    • On a quadrature formula for trigonometric integrals
    • Filon L.N.G. On a quadrature formula for trigonometric integrals. Proc. Roy Soc. Edinburgh 49 (1928) 38-47
    • (1928) Proc. Roy Soc. Edinburgh , vol.49 , pp. 38-47
    • Filon, L.N.G.1
  • 15
    • 4043159167 scopus 로고    scopus 로고
    • On the numerical quadrature of highly-oscillating integrals I: Fourier transforms
    • Iserles A. On the numerical quadrature of highly-oscillating integrals I: Fourier transforms. IMA J. Numer. Anal. 24 (2004) 365-391
    • (2004) IMA J. Numer. Anal. , vol.24 , pp. 365-391
    • Iserles, A.1
  • 16
    • 11444264626 scopus 로고    scopus 로고
    • On the numerical quadrature of highly-oscillating integrals II: Irregular oscillators
    • Iserles A. On the numerical quadrature of highly-oscillating integrals II: Irregular oscillators. IMA J. Numer. Anal. 25 (2005) 25-44
    • (2005) IMA J. Numer. Anal. , vol.25 , pp. 25-44
    • Iserles, A.1
  • 17
    • 18244376597 scopus 로고    scopus 로고
    • On quadrature methods for highly oscillatory integrals and their implementation
    • Iserles A., and Nørsett S.P. On quadrature methods for highly oscillatory integrals and their implementation. BIT 44 (2004) 755-772
    • (2004) BIT , vol.44 , pp. 755-772
    • Iserles, A.1    Nørsett, S.P.2
  • 18
    • 26944452051 scopus 로고    scopus 로고
    • Efficient quadrature of highly-oscillatory integrals using derivatives
    • Iserles A., and Nørsett S.P. Efficient quadrature of highly-oscillatory integrals using derivatives. Proc. Roy. Soc. A 461 (2005) 1383-1399
    • (2005) Proc. Roy. Soc. A , vol.461 , pp. 1383-1399
    • Iserles, A.1    Nørsett, S.P.2
  • 19
    • 84968468712 scopus 로고
    • Procedures for computing one-and-two dimensional integrals of functions with rapid irregular oscillations
    • Levin D. Procedures for computing one-and-two dimensional integrals of functions with rapid irregular oscillations. Math. Comp. 38 (1982) 531-538
    • (1982) Math. Comp. , vol.38 , pp. 531-538
    • Levin, D.1
  • 20
    • 84968470212 scopus 로고
    • An algorithm for the machine calculation of complex Fourier series
    • Cooley J.W., and Tukey J.W. An algorithm for the machine calculation of complex Fourier series. Math. Comp. 19 (1965) 297-301
    • (1965) Math. Comp. , vol.19 , pp. 297-301
    • Cooley, J.W.1    Tukey, J.W.2
  • 22
    • 0033456757 scopus 로고    scopus 로고
    • A construction of interpolating wavelets on invariant sets
    • Chen Z., Micchelli C.A., and Xu Y. A construction of interpolating wavelets on invariant sets. Math. Comp. 68 (1999) 1569-1587
    • (1999) Math. Comp. , vol.68 , pp. 1569-1587
    • Chen, Z.1    Micchelli, C.A.2    Xu, Y.3
  • 23
    • 0042745034 scopus 로고    scopus 로고
    • A construction of refinable sets for interpolating wavelets
    • Micchelli C.A., Sauer T., and Xu Y. A construction of refinable sets for interpolating wavelets. Result. Math. 34 (1998) 359-372
    • (1998) Result. Math. , vol.34 , pp. 359-372
    • Micchelli, C.A.1    Sauer, T.2    Xu, Y.3
  • 25
    • 0141956329 scopus 로고    scopus 로고
    • Higher order sparse grids methods for elliptic partial differential equations with variable coefficients
    • Achatz S., and München. Higher order sparse grids methods for elliptic partial differential equations with variable coefficients. Computing 71 (2003) 1-15
    • (2003) Computing , vol.71 , pp. 1-15
    • Achatz, S.1    München2
  • 27
    • 0006804542 scopus 로고    scopus 로고
    • Sparse grids: Recent developments for elliptic partial differential equations
    • Hackbusch W., and Wittum G. (Eds), Springer, Berlin/Heidelberg
    • Bungartz H.-J., and Dornseifer T. Sparse grids: Recent developments for elliptic partial differential equations. In: Hackbusch W., and Wittum G. (Eds). Multigrid Methods V (1998), Springer, Berlin/Heidelberg 45-70
    • (1998) Multigrid Methods V , pp. 45-70
    • Bungartz, H.-J.1    Dornseifer, T.2
  • 28
    • 34547961823 scopus 로고    scopus 로고
    • Two-scale Boolean Galerkin discretizations for Fredholm integral equations of the second kind
    • Liu F., and Zhou A. Two-scale Boolean Galerkin discretizations for Fredholm integral equations of the second kind. SIAM J. Numer. Anal. 45 (2007) 296-312
    • (2007) SIAM J. Numer. Anal. , vol.45 , pp. 296-312
    • Liu, F.1    Zhou, A.2
  • 29
    • 11944265109 scopus 로고    scopus 로고
    • Sparse approximation of singularity functions
    • Nitsche P. Sparse approximation of singularity functions. Constr. Approx. 21 (2005) 63-81
    • (2005) Constr. Approx. , vol.21 , pp. 63-81
    • Nitsche, P.1
  • 31
    • 36248953145 scopus 로고    scopus 로고
    • Fast Boolean approximation methods for solving integral equations in high dimensions
    • Xu Y., and Zhou A. Fast Boolean approximation methods for solving integral equations in high dimensions. J. Integral Equations Appl. 16 (2004) 83-110
    • (2004) J. Integral Equations Appl. , vol.16 , pp. 83-110
    • Xu, Y.1    Zhou, A.2
  • 33
    • 33751218044 scopus 로고    scopus 로고
    • Fast algorithms for spherical harmonic expansions
    • Rokhlin V., and Tygert M. Fast algorithms for spherical harmonic expansions. SIAM J. Sci. Comput. 27 (2006) 1903-1928
    • (2006) SIAM J. Sci. Comput. , vol.27 , pp. 1903-1928
    • Rokhlin, V.1    Tygert, M.2
  • 35
    • 0023289278 scopus 로고
    • Lattice methods for multiple integration: Theory, error analysis and examples
    • Sloan I., and Kachoyan P. Lattice methods for multiple integration: Theory, error analysis and examples. SIAM J. Numer. Anal. 24 (1987) 116-128
    • (1987) SIAM J. Numer. Anal. , vol.24 , pp. 116-128
    • Sloan, I.1    Kachoyan, P.2
  • 38
    • 0033279290 scopus 로고    scopus 로고
    • Fast algorithms for spline wavelets on sparse grids
    • Bittner K. Fast algorithms for spline wavelets on sparse grids. SIAM J. Sci. Comput. 20 (1999) 1192-1213
    • (1999) SIAM J. Sci. Comput. , vol.20 , pp. 1192-1213
    • Bittner, K.1
  • 39
    • 0034381734 scopus 로고    scopus 로고
    • High dimensional polynomial interpolation on sparse grids
    • Barthelmann V., Novak E., and Ritter K. High dimensional polynomial interpolation on sparse grids. Adv. Comput. Math. 12 (2000) 273-288
    • (2000) Adv. Comput. Math. , vol.12 , pp. 273-288
    • Barthelmann, V.1    Novak, E.2    Ritter, K.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.