메뉴 건너뛰기




Volumn 24, Issue 3, 2008, Pages 269-289

New efficient methods of computing the prolate spheroidal wave functions and their corresponding eigenvalues

Author keywords

Bessel functions; Finite Fourier transform; Legendre polynomials; Prolate spheroidal wave functions

Indexed keywords

ASYMPTOTIC ANALYSIS; BESSEL FUNCTIONS; COMPUTATIONAL EFFICIENCY; EIGENVALUES AND EIGENFUNCTIONS; FOURIER TRANSFORMS; NUMERICAL METHODS; POLYNOMIALS;

EID: 41349106962     PISSN: 10635203     EISSN: 1096603X     Source Type: Journal    
DOI: 10.1016/j.acha.2007.06.004     Document Type: Article
Times cited : (49)

References (21)
  • 1
    • 41349091489 scopus 로고
    • Norms and exclusions
    • Bauer F.L., and Fike C.T. Norms and exclusions. Numer. Math. 2 (1960) 123-144
    • (1960) Numer. Math. , vol.2 , pp. 123-144
    • Bauer, F.L.1    Fike, C.T.2
  • 2
    • 0002237285 scopus 로고
    • Irregular sampling and frames
    • Chui C.K. (Ed), Academic Press, New York
    • Benedetto J. Irregular sampling and frames. In: Chui C.K. (Ed). Wavelets: A Tutorial in Theory and Applications (1992), Academic Press, New York 445-507
    • (1992) Wavelets: A Tutorial in Theory and Applications , pp. 445-507
    • Benedetto, J.1
  • 3
    • 3943060186 scopus 로고    scopus 로고
    • On generalized Gaussian quadrature for exponentials and their applications
    • Beylkin G., and Monzon L. On generalized Gaussian quadrature for exponentials and their applications. Appl. Comput. Harmon. Anal. 12 (2002) 332-373
    • (2002) Appl. Comput. Harmon. Anal. , vol.12 , pp. 332-373
    • Beylkin, G.1    Monzon, L.2
  • 4
    • 13444255982 scopus 로고    scopus 로고
    • Wave propagation using bases for band-limited functions
    • Beylkin G., and Sandberg K. Wave propagation using bases for band-limited functions. Wave Motion 41 (2005) 263-291
    • (2005) Wave Motion , vol.41 , pp. 263-291
    • Beylkin, G.1    Sandberg, K.2
  • 5
    • 4544383537 scopus 로고    scopus 로고
    • Prolate spheroidal wave functions as an alternative to Chebyshev and Legendre polynomials for spectral element and pseudo-spectral algorithms
    • Boyd J.P. Prolate spheroidal wave functions as an alternative to Chebyshev and Legendre polynomials for spectral element and pseudo-spectral algorithms. J. Comput. Phys. 199 (2004) 688-716
    • (2004) J. Comput. Phys. , vol.199 , pp. 688-716
    • Boyd, J.P.1
  • 6
    • 0347480334 scopus 로고    scopus 로고
    • Approximation of an analytic function on a finite real interval by a band-limited function and conjectures on properties of prolate spheroidal functions
    • Boyd J.P. Approximation of an analytic function on a finite real interval by a band-limited function and conjectures on properties of prolate spheroidal functions. Appl. Comput. Harmon. Anal. 15 (2003) 168-176
    • (2003) Appl. Comput. Harmon. Anal. , vol.15 , pp. 168-176
    • Boyd, J.P.1
  • 7
    • 84950242370 scopus 로고
    • English edition translated from the German original, Wiley Interscience Publishers, New York
    • Courant R., and Hilbert D. Methods of Mathematical Physics, vol. 1. English edition translated from the German original (1989), Wiley Interscience Publishers, New York
    • (1989) Methods of Mathematical Physics, vol. 1
    • Courant, R.1    Hilbert, D.2
  • 10
    • 0142260921 scopus 로고    scopus 로고
    • Sampling theory approach to prolate spheroidal wave functions
    • Khare K., and George N. Sampling theory approach to prolate spheroidal wave functions. J. Phys. A Math. Gen. 36 (2003) 10011-10021
    • (2003) J. Phys. A Math. Gen. , vol.36 , pp. 10011-10021
    • Khare, K.1    George, N.2
  • 11
    • 84857887285 scopus 로고
    • Prolate spheroidal wave functions, Fourier analysis and uncertainty-II
    • Landau H.J., and Pollak H.O. Prolate spheroidal wave functions, Fourier analysis and uncertainty-II. Bell System Tech. J. 40 (1961) 65-84
    • (1961) Bell System Tech. J. , vol.40 , pp. 65-84
    • Landau, H.J.1    Pollak, H.O.2
  • 12
    • 84944487979 scopus 로고
    • Prolate spheroidal wave functions, Fourier analysis and uncertainty-III. The dimension of space of essentially time- and band-limited signals
    • Landau H.J., and Pollak H.O. Prolate spheroidal wave functions, Fourier analysis and uncertainty-III. The dimension of space of essentially time- and band-limited signals. Bell System Tech. J. 41 (1962) 1295-1336
    • (1962) Bell System Tech. J. , vol.41 , pp. 1295-1336
    • Landau, H.J.1    Pollak, H.O.2
  • 13
    • 2442585496 scopus 로고    scopus 로고
    • Prolate spheroidal wave functions, an introduction to the Slepian series and its properties
    • Moore I.C., and Cada M. Prolate spheroidal wave functions, an introduction to the Slepian series and its properties. Appl. Comput. Harmon. Anal. 16 (2004) 208-230
    • (2004) Appl. Comput. Harmon. Anal. , vol.16 , pp. 208-230
    • Moore, I.C.1    Cada, M.2
  • 14
    • 2442430339 scopus 로고    scopus 로고
    • Wavelets based on prolate spheroidal wave functions
    • Walter G., and Shen X. Wavelets based on prolate spheroidal wave functions. J. Fourier Anal. Appl. 10 (2004) 1-25
    • (2004) J. Fourier Anal. Appl. , vol.10 , pp. 1-25
    • Walter, G.1    Shen, X.2
  • 15
    • 13844276742 scopus 로고    scopus 로고
    • Prolate spheroidal wavelets: Translation, convolution and differentiation made easy
    • Walter G. Prolate spheroidal wavelets: Translation, convolution and differentiation made easy. J. Fourier Anal. Appl. 11 (2005) 73-84
    • (2005) J. Fourier Anal. Appl. , vol.11 , pp. 73-84
    • Walter, G.1
  • 16
    • 27844440802 scopus 로고    scopus 로고
    • A new friendly method of computing prolate spheroidal wave functions and wavelets
    • Walter G., and Soleski T. A new friendly method of computing prolate spheroidal wave functions and wavelets. Appl. Comput. Harmon. Anal. 19 (2005) 432-443
    • (2005) Appl. Comput. Harmon. Anal. , vol.19 , pp. 432-443
    • Walter, G.1    Soleski, T.2
  • 17
    • 84939751170 scopus 로고
    • Prolate spheroidal wave functions, Fourier analysis and uncertainty I
    • Slepian D., and Pollak H.O. Prolate spheroidal wave functions, Fourier analysis and uncertainty I. Bell System Tech. J. 40 (1961) 43-64
    • (1961) Bell System Tech. J. , vol.40 , pp. 43-64
    • Slepian, D.1    Pollak, H.O.2
  • 18
    • 0020786063 scopus 로고
    • Some comments on Fourier analysis, uncertainty and modeling
    • Slepian D. Some comments on Fourier analysis, uncertainty and modeling. SIAM Rev. 25 (1983) 379-393
    • (1983) SIAM Rev. , vol.25 , pp. 379-393
    • Slepian, D.1
  • 19
    • 0035420586 scopus 로고    scopus 로고
    • Prolate spheroidal wave functions, quadrature and interpolation
    • Xiao H., Rokhlin V., and Yarvin N. Prolate spheroidal wave functions, quadrature and interpolation. Inverse Problems 17 (2001) 805-838
    • (2001) Inverse Problems , vol.17 , pp. 805-838
    • Xiao, H.1    Rokhlin, V.2    Yarvin, N.3
  • 20
    • 0742323822 scopus 로고    scopus 로고
    • High-frequency asymptotic expansions for certain prolate spheroidal wave functions
    • Xiao H., and Rokhlin V. High-frequency asymptotic expansions for certain prolate spheroidal wave functions. J. Fourier Anal. Appl. 9 (2003) 575-596
    • (2003) J. Fourier Anal. Appl. , vol.9 , pp. 575-596
    • Xiao, H.1    Rokhlin, V.2
  • 21
    • 33751002629 scopus 로고    scopus 로고
    • Approximate formulae for certain prolate spheroidal wave functions valid for large values of both order and band-limit
    • Rokhlin V., and Xiao H. Approximate formulae for certain prolate spheroidal wave functions valid for large values of both order and band-limit. Appl. Comput. Harmon. Anal. 22 (2007) 105-123
    • (2007) Appl. Comput. Harmon. Anal. , vol.22 , pp. 105-123
    • Rokhlin, V.1    Xiao, H.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.