フーリエ・ルジャンドル法の誤差特性  [in Japanese] Error Characteristic of the Fourier-Legendre Method  [in Japanese]

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Abstract

Error characteristics of the Fourier expansion of the Legendre polynomials are examined in the computation of the Gaussian latitudes and weights and in the Fourier– Legendre scaling factor for associated Legendre functions. The Fourier–Newton method yields values accurate enough for practical use up to 10000 nodes. Because the relative error grows in O(𝑛) and the computational complexity in O(𝑛"), alternative methods may be required for larger calculation. There is a room for improvement in the computation of the Fourier–Legendre coefficients. The Fourier–Legendre scaling factor is not necessary in the computation of the Gaussian latitudes and weights, but for associated Legendre functions. The accuracy can be improved significantly by use of alternative equations or the asymptotic series of the Gamma function.

Journal

  • 京都大学防災研究所年報 = DPRI annuals

    京都大学防災研究所年報 = DPRI annuals (59), 153-158, 2015

    京都大学防災研究所

Codes

  • NII Article ID (NAID)
    120005867087
  • NII NACSIS-CAT ID (NCID)
    AN00027786
  • Text Lang
    JPN
  • Article Type
    departmental bulletin paper
  • Journal Type
    大学紀要
  • ISSN
    0386-412X
  • NDL Article ID
    027652870
  • NDL Call No.
    YH247-547
  • Data Source
    NDL  IR 
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