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| 超高阶次勒让德函数递推计算中的压缩因子和Horner求和技术 | |
| 引用本文： | 刘缵武,刘世晗,黄欧. 超高阶次勒让德函数递推计算中的压缩因子和Horner求和技术[J]. 测绘学报, 2011, 40(4): 454-458 |
| 作者姓名： | 刘缵武 刘世晗 黄欧 |
| 作者单位： | 1. 信息工程大学理学院,河南郑州,450001 2. 郑州市市政工程总公司,河南郑州,450007 3. 美国俄亥俄州立大学地球科学学院,俄亥俄哥伦布43210 |
| 基金项目： | 国家自然科学基金(41074015) |
| 摘 要： | 超过2 000阶次的缔合勒让德函数值的递推计算,在接近两极时达到极大的数量级（超过10的数千次方）,这导致现有递推方法在计算缔合勒让德函数值及其导数值时失效。通过插入压缩因子技术,提出一个修改的递推算法,并结合使用Horner求和技术计算球谐级数的部分和。试验表明,该算法至少可以计算到3 600完全阶次的球谐级数式,优于现有结果。 |
| 关 键 词： | 缔合勒让德函数 递推公式 压缩因子 球谐级数 Horner求和技术 |
Scale Factors in Recursion of Ultra-high Degree and Order Legendre Functions and Horner's Scheme of Summation |
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| LIU Zuanwu,LIU Shihan,HUANG Ou. Scale Factors in Recursion of Ultra-high Degree and Order Legendre Functions and Horner's Scheme of Summation[J]. Acta Geodaetica et Cartographica Sinica, 2011, 40(4): 454-458 | |
| Authors: | LIU Zuanwu LIU Shihan HUANG Ou |
| Affiliation: | LIU Zuanwu1,LIU Shihan2,HUANG Ou3 1.Institute of Science,Information Engineering University,Zhengzhou 450001,China,2.Zhengzhou General Company of Municipality Engineering,Zhengzhou 450007,3.School of Earth Sciences,Ohio State University,Columbus,Ohio 43210,USA |
| Abstract: | When evaluated increasingly close to the poles,the computations of the very high degree and order(e.g.over 2 000) associated Legendre functions exhibit extremely large ranges(over thousands of orders) of magnitudes.This causes existing recursion techniques for computing values of associated Legendre functions and their derivatives to fail.A modified recursion algorithm is proposed for computing associated Legendre functions and their first derivatives by a scale factor.The modified recursions yield scaled a... |
| Keywords: | associated Legendre functions recursion formulas scale factor spherical harmonic series Horner's scheme |
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