CONTRASTIVE ANALYSIS OF COMMON COMPUTING METHODSOF ULTRAHIGH DEGREE AND ORDER FULLY NORMALIZED ASSOCIATED LEGENDRE FUNCTION
Wang Jianqiang 1) ; Zhao Guoqiang 2) ; and Zhu Guangbin 1)
1)School of Geodesy and Geomatics, Wuhan University, Wuhan 4300792)Institute of Earthquake Science, CEA, Beijing 100036
Abstract The numerical stability of the construction and application of the ultrahigh degree and order earth’s gravity model lies on the computing methods of the ultrahigh degree and order normalized associated legendre functions (ALFs). Four computing methods of ALFs including standard forward column method, standard forward row method, Belikov column method and recursive method between every other order and degree, are discussed and their calculation programs are improvied. Advantages and disadvantages of these methods are analyzed and compared in two aspects: numerical efficiency and numerical accuracy, when the degree and order are up to 3 060. Numerical tests prove that recursive method between every other order and degree is excellent.
Key words ：
fully normalized associated legendre function
recursive method between every other order and degree
spherical harmonic synthesis
spherical harmonic analysis
stability
Received: 01 January 1900
Corresponding Authors:
Wang Jianqiang
Cite this article:
Wang Jianqiang ,Zhao Guoqiang ,and Zhu Guangbin . CONTRASTIVE ANALYSIS OF COMMON COMPUTING METHODSOF ULTRAHIGH DEGREE AND ORDER FULLY NORMALIZED ASSOCIATED LEGENDRE FUNCTION[J]. , 2009, 29(2): 126-130.
Wang Jianqiang ,Zhao Guoqiang ,and Zhu Guangbin . CONTRASTIVE ANALYSIS OF COMMON COMPUTING METHODSOF ULTRAHIGH DEGREE AND ORDER FULLY NORMALIZED ASSOCIATED LEGENDRE FUNCTION[J]. jgg, 2009, 29(2): 126-130.
URL:
http://www.jgg09.com/EN/ OR http://www.jgg09.com/EN/Y2009/V29/I2/126
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