【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。更多还原

【Abstract】 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.更多还原