大地测量与地球动力学2013，Vol.33Issue(1)：40-44,5.
总体最小二乘的扰动分析
RESEARCH ON PERTURBATION ANALYSIS OF THE TOTAL LEAST SQUARES
摘要
Abstract
On the basis of the condition number definition of coefficient matrix and from the viewpoint of numerical analysis, the perturbation analysis equations of least squares ( LS) and data least squares ( DLS) are deduced , in following cases when the perturbation is only contained in the observation data, the perturbations are contained in the observation data and coefficient matrix, and the perturbation is only contained in the coefficient matrix. On the basis of the closed-form expression of the total least squares (TLS) solution and with the tool of the singular value decomposition (SVD) , the perturbation analysis equation of TLS is deduced. Through the analysis, the perturbation analysis equation of TLS is the unified form of the perturbation analysis equation of LS and DLS.关键词
总体最小二乘/最小二乘/数据最小二乘/扰动分析/条件数Key words
total least squares (TLS)/least squares ( LS)/data least squares (DLS)/perturbation analysis/condition number分类
天文与地球科学引用本文复制引用
王乐洋..总体最小二乘的扰动分析[J].大地测量与地球动力学,2013,33(1):40-44,5.基金项目
国家自然科学基金(41204003) （41204003）
东华理工大学博士科研启动基金(DHBK201113) （DHBK201113）
江西省数字国土重点实验室开放研究基金(DLLJ201207) （DLLJ201207）
