摘要
本文在分析自由网解算方法的基础上,探讨了矩阵的奇异值分解和广义逆矩阵的关系,证明了奇异分解和广义逆矩阵的关系,推导了应用奇异分解进行自由网平差解算的公式,给出了加权情况下自由网平差的奇异值分解解算。最后通过算例进行了解算,验证了方法的正确性和合理性。通过奇异值分解分析可以看出矩阵分解在测量平差解算中的特殊作用,揭示了矩阵分解和平差计算的关系。
Based on the analysis of free network adjustment, the relationship between Singular Value Decomposition（SVD） and Moore-Penrose inverses is discussed here and also testified by the authors of this paper The formulae of free network based on matrix singular value decomposition and the formulaes on the case of additional different weight are all presented. Finally, apractical computation has proved that the SVD method is correct and effective for free network adjustment .From this paper,the special function of matrix decomposition in surveying data processing is found out and the relationship between matrix decomposition and adjustment also released.
出处
《工程勘察》
CSCD
北大核心
2008年第4期43-45,60,共4页
Geotechnical Investigation & Surveying
基金
国家自然科学基金资助项目(40574008)
江西省自然科学基金资助项目(0411005)
江西省教育厅科技资助项目(赣教财2006[208])
地球空间环境与大地测量教育部重点实验室开放基金资助项目(04-01-07)
数字国土江西省重点实验室开放基金资助项目(DLLJ200506)
地理空间信息工程国家测绘局重点实验室开放基金资助项目.
关键词
矩阵分解
自由网
最小范数最小二乘解
测量平差
matrix decomposition
free network
minimum norm least squares
surveying adjustment
