摘要
为了解决最小二乘配置解算问题,采用QR分解解法建立了直接解算算法。分析了目前采用的最小二乘配置法解算方法,在讨论了矩阵的QR分解方法的基础上,推导得出了矩阵QR分解与广义逆矩阵的关系,得出了可以直接利用QR分解求解矩阵的最小二乘逆,并推导了应用QR分解求解最小二乘配置的估值计算公式和精度估算公式,最后通过重力异常实例进行了计算,得出矩阵的QR分解用于最小二乘配置解算的正确性和可行性。该成果为最小二乘配置法提供了一种新的解算方法。
In order to calculate the least square collocation model, a direct algorithm is proposed based on matrix QR decomposition. This paper overviews the various algorithms for least square collocation, discusses the matrix QR decomposition, derives the relationship between QR decomposition and generalized inverse matrix, and obtains least square inverse used for calculating matrix. In addition, the estimation formula for least square collocation by QR decomposition and its accuracy formula are derived. A case study is conducted using gravity anomaly test and calculation to demonstrate that the QR method is correct and valid in least-square collocation calculation. The method presented in this paper provides a new tool for least-squares collocation calculation.
出处
《辽宁工程技术大学学报（自然科学版）》
CAS
北大核心
2009年第4期550-553,共4页
Journal of Liaoning Technical University (Natural Science)
基金
国家自然科学基金资助项目(40874010
40574008)
江西省自然科学基金资助项目(2007GZC0474)
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(06-06)
数字国土江西省重点实验室开放基金资助项目(DLLJ200506)
关键词
最小二乘配置
矩阵分解
重力异常
least square collocation
matrix decomposition
gravity anomaly
