%0 Journal Article
%T CHARACTERISTICS OF MATRIX SVD AND ITS APPLICATIONS TO RANK DEFICIENCY FREE NETWORK ADJUSTMENT<br>矩阵的SVD分解性质及其在秩亏网平差中的应用
%A Lu Tieding
%A Tao Benzao
%A Zhou Shijian
%A <br>鲁铁定
%A 陶本藻
%A 周世健
%J 大地测量与地球动力学
%D 2007
%I 
%X The matrix SVD(Singular Value Decomposition) and the relation between SVD and Moore-Penrose inverses are analyzed. It is derived that the generalize inverse matrix of SVD is Moore-Penrose 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.
%K SVD(Singular Value Decomposition)
%K matrix decompositions
%K rank deficiency free network
%K generalized inverse matrix
%K surveying adjustment<br>奇异值分解
%K 矩阵分解
%K 秩亏网
%K 广义逆矩阵
%K 测量平差
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=E62459D214FD64A3C8082E4ED1ABABED5711027BBBDDD35B&cid=DA72A78627FE64EAA572951EA05D274A&jid=73A1A428591E600EF664B596512A2997&aid=D8051B66BB891A2E39D9F05AC8932A5C&yid=A732AF04DDA03BB3&vid=DB817633AA4F79B9&iid=94C357A881DFC066&sid=E84BBBDDD74F497C&eid=5D71B28100102720&journal_id=1671-5942&journal_name=大地测量与地球动力学&referenced_num=0&reference_num=18