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| 引用本文： | 唐利民,朱建军.?????????????С????????????????????????[J].大地测量与地球动力学,2010,30(6):51-56. |
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| 作者姓名： | 唐利民 朱建军 |
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| 作者单位： | 1. 中南大学信息物理工程学院,长沙,410083;长沙理工大学交通运输工程学院,长沙,410004
2. 中南大学信息物理工程学院,长沙,410083 |
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| 基金项目： | 国家自然科学基金，湖南省科技计划项目 |
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| 摘 要： | ???????????????????????Jacobian???????????????????????????????С?????????????????????????С?????????????????????????в?????????С??ж?????????????????????2??????????????????仮??????????????????С??????????н???????????÷???????????????????????????????????????????????????????????????????????????????????????????????????????????С??????????????С??????
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| 关 键 词： | ?????????????С???????? ??????? ????????? ???仮??? ?????????????????? |
REGULARIZATION HOMOTOPY METHOD FOR SOLVING ILL-POSED NONLINEAR LEAST SQUARE PROBLEM AND ITS APPLICATION |
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| Tang Limin,Zhu Jianjun.REGULARIZATION HOMOTOPY METHOD FOR SOLVING ILL-POSED NONLINEAR LEAST SQUARE PROBLEM AND ITS APPLICATION[J].Journal of Geodesy and Geodynamics,2010,30(6):51-56. |
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| Authors: | Tang Limin Zhu Jianjun |
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| Institution: | 1)School of Info-Physics and Geomatics Engineering of Central South University, Changsha 4100832)School of Traffic and Transportation Engineering, Changsha University of Science &; Technology, Changsha 410004 |
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| Abstract: | A regularization homotopy function is constructed for solving the ill posed nonlinear least squares problem whose Jacobian matrix is rank deficient or very ill conditioned. A regularization homotopy iterative formula is established for ill posed nonlinear least squares problem. The iterative process is derived in detial and the continuity and convergence conditions are given as well. Two new regularization parameter selecting strategies are proposed, which called as direct search method and interval division method. The calculation results of nonlinear least squares problems show that the method is correctly and applicable. Calculation results of nonlinear adjustment of free networks with rank deficiency examples also show that the method not only decrease the iterative matrix condition number, but also make the condition number small fluctuation in the total iterative process, so that a smaller stable norm solution can be obtained. |
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| Keywords: | ill psoed nonlinear least squares problem regularization homotopy direct search method interval division method nonlinear adjustment of free networks with rank deficiency |
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