CHARACTERISTICS OF MATRIX SVD AND ITS APPLICATIONS TO RANK DEFICIENCY FREE NETWORK ADJUSTMENT
Lu Tieding 1,2) ;Tao Benzao 1) ;and Zhou Shijian 1,3)
1)School of Geodesy and Geomatics ,Wuhan university,Wuhan 4300792)School of Geoscience and Surveying Engineering,East China Institute of Technology,Fuzhou 3440003)Jiangxi Academy of Science, Nanchang 330029
Abstract The matrix SVD(Singular Value Decomposition) and the relation between SVD and MoorePenrose inverses are analyzed. It is derived that the generalize inverse matrix of SVD is MoorePenrose generalized inverse of the matrix namely.The relation between the SVD and the minimum norm least squares solution of linear system of equation is also analyzed and the formulas of free network adjustment based on matrix singular value decomposition are presented. The formulas for solving weighted minimum norm least squares are also presented, which expanded the minimum norm least squares solution of linear system of equation based on matrix SVD. The practical computations show that the SVD method is correct and validity in free network adjustment. \
Lu Tieding,Tao Benzao ,and Zhou Shijian. CHARACTERISTICS OF MATRIX SVD AND ITS APPLICATIONS TO RANK DEFICIENCY FREE NETWORK ADJUSTMENT[J]. , 2007, 27(5): 63-67.
Lu Tieding,Tao Benzao ,and Zhou Shijian. CHARACTERISTICS OF MATRIX SVD AND ITS APPLICATIONS TO RANK DEFICIENCY FREE NETWORK ADJUSTMENT[J]. jgg, 2007, 27(5): 63-67.
