| 基于矩阵分解理论的秩亏网平差 |
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| 引用本文： | 夏立福,李井春.基于矩阵分解理论的秩亏网平差[J].海洋测绘,2009,29(1):21-24. |
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| 作者姓名： | 夏立福 李井春 |
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| 作者单位： | 1. 中国地质大学,测绘工程学院,湖北,武汉,430074
2. 武汉大学,测绘学院,湖北,武汉,430079 |
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| 摘 要： | 对矩阵的最大秩分解、奇异值分解进行了分析，将两种分解方法应用于秩亏网平差中，得到新的未知量平差结果和精度评定公式，其形式更利于计算机语言编程；同时推导证明了奇异值分解和M—P广义逆矩阵之间的关系，得出奇异值分解的广义逆矩眸为矩阵的M—P广义逆；最后通过秩亏网算例进行了解算，验证了方法的正确性和矩阵分解的有效性。
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| 关 键 词： | 矩阵分解 最大秩分解 奇异值分解 秩亏网平差 |
Rank defect Net Adjustment Based on Theory of Matrix Factorization |
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| XIA Li-fu,LI Jing-chun.Rank defect Net Adjustment Based on Theory of Matrix Factorization[J].Hydrographic Surveying and Charting,2009,29(1):21-24. |
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| Authors: | XIA Li-fu LI Jing-chun |
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| Institution: | 1.Information Engineering Institute of China University of Geosciences;Wuhan;Hubei;430074;2.School of Geodesy and Geomatics;Wuhan University;430079 |
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| Abstract: | Maximum rank resolving and the matrix SVD are deeply analyzed,two kinds of decomposition methodare used in rank-defect net adjustment,we obtain the new unknown quantity adjustment results and assessing the formula for precision.Its form is suitable for the machine language programming.At the same time,the matrix SVD 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.At last,the... |
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| Keywords: | matrix factorization maximum rank resolving the matrix SVD rank-defect net adjustment |
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