| 超高阶球谐级数式的计算方法 |
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| 引用本文： | 刘缵武,刘世晗,张敬伟.超高阶球谐级数式的计算方法[J].数学的实践与认识,2012,42(9):178-181. |
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| 作者姓名： | 刘缵武 刘世晗 张敬伟 |
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| 作者单位： | 1. 信息工程大学理学院,河南 郑州,450052
2. 河南建筑职业技术学院土木工程系,河南郑州,450007 |
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| 摘 要： | 由完全正常化缔合勒让德函数构成的球谐级数式,在接近两极时,超高阶次(如超过2500阶次)缔合勒让德函数值的递推计算,达到极大的数量级(超过10的数千次方),产生下溢,这导致一般递推方法失效.本文就缔合勒让德函数的4种常用递推算法,分别进行改进以增加数值稳定性并延缓下溢.最后对由改进算法获得的勒让德函数,结合Horner求和技术,给出计算超高阶球谐级数部分和式的方法.
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| 关 键 词： | 缔合勒让德函数 递推算法 延缓溢出 球谐级数 |
Methods of Computing Ultra-high Degree Spherical Harmonic Series |
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| LIU Zuan-wu
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LIU Shi-han
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ZHANG Jing-wei.Methods of Computing Ultra-high Degree Spherical Harmonic Series[J].Mathematics in Practice and Theory,2012,42(9):178-181. |
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| Authors: | LIU Zuan-wu LIU Shi-han ZHANG Jing-wei |
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| Institution: | 1.Institute of science,Information Engineering University,Zhengzhou 450052,China) (2.Depatment of Civil Engineering,Henan Technical College of Construction,Zhengzhou 450007,China) |
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| Abstract: | Spherical harmonic series form sums of fully normalised associated Legendre .functions(ALFs).However,when evaluated increasingly close to the poles,the ultra-high degree and order(e.g.2500) ALFs range over thousands of orders of magnitude,the computed value of ALFs will underflow and be set to zero.This causes usual recursion techniques for computing values of ALFs to fail.Four methods of computing ALFs are discussed and improved for the numerrical stability and delaying underflow,the modified recursions yield scaled ALFs,which can then be combined using Horner’s scheme to compute partial sums. |
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| Keywords: | Legendre functions recursion algorithm delaying underflow spherical harmonic series |
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