Numerical computation of spherical harmonics of arbitrary degree and order by extending exponent of floating point numbers: III integral

被引：11

作者：

Fukushima, Toshio ^{[1
]}

机构：

[1] Natl Inst Nat Sci, Natl Astron Observ Japan, Mitaka, Tokyo 1818588, Japan

来源：

COMPUTERS & GEOSCIENCES | 2014年 / 63卷

关键词：

Exponent extension; Forward recursion; Integral of associated Legendre functions; Spherical harmonic analysis; Underflow problem;

D O I：

10.1016/j.cageo.2013.10.010

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

The integrals of fully normalized associated Legendre function (fnALF) of extremely high degree and order such as 2(23) = 8 388 608 can be obtained without underflow problems if the point values of fnALF are properly given by using an exponent extension of the floating point numbers (Fukushima, T., 2012a. J. Geod., 86, 271-285; Fukushima, T., 2012c. J. Geod., 86, 1019-1028). A dynamic termination of the exponent extension during the fixed-order increasing-degree recursions significantly reduces the increase in CPU time caused by the exponent extension. Also, the sectorial integrals are found to be correctly obtained by the forward recursion only even when the backward recursion has been claimed to be necessary (Paul, M.K., 1978, Bull. Geod., 52, 177-190; Gerstl, M., 1980, Manuscr. Geod., 5, 181-199). (C) 2013 Elsevier Ltd. All rights reserved.

引用

页码：17 / 21

页数：5

共 5 条

[1] Numerical computation of spherical harmonics of arbitrary degree and order by extending exponent of floating point numbers
Toshio Fukushima
[J]. Journal of Geodesy, 2012, 86 : 271 - 285
[2] Numerical computation of spherical harmonics of arbitrary degree and order by extending exponent of floating point numbers
Fukushima, Toshio
[J]. JOURNAL OF GEODESY, 2012, 86 (04) : 271 - 285
[3] Numerical computation of spherical harmonics of arbitrary degree and order by extending exponent of floating point numbers: II first-, second-, and third-order derivatives
Fukushima, Toshio
[J]. JOURNAL OF GEODESY, 2012, 86 (11) : 1019 - 1028
[4] Numerical computation of spherical harmonics of arbitrary degree and order by extending exponent of floating point numbers: II first-, second-, and third-order derivatives
Toshio Fukushima
[J]. Journal of Geodesy, 2012, 86 : 1019 - 1028
[5] Numerical Computation of Point Values, Derivatives, and Integrals of Associated Legendre Function of the First Kind and Point Values and Derivatives of Oblate Spheroidal Harmonics of the Second Kind of High Degree and Order
Fukushima, Toshio
[J]. IAG 150 YEARS, 2016, 143 : 193 - 197

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