Acta Geodaetica et Cartographica Sinica

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The Perturbation Analysis of Nonlinear Ill-conditioned Solution

  

  • Received:2009-09-25 Revised:2010-03-31 Online:2011-02-25 Published:2011-02-25

Abstract: In addition to the ill-conditioned analysis of the nonlinear model itself, the perturbation stemmed from truncation and orthogonalization process needs to be considered. In this paper, the perturbative estimation inequality of nonlinear ill-conditioned problem was derived from the definition of the generalized condition number. And based on the perturbative estimation inequality, the impacts of judgement and analysis were studied on nonlinear ill-conditioned problem. The impacts stemmed primarily from the disturbance of the coefficient matrix of linear approximation and additional truncation error,also including orthogonal approximation. Therefore, nonlinear ill-conditioned problem was verified and analyzed through two examples. The results of the research show that: when the model nonlinearity is strong, the disturbance of the coefficient matrix and additional truncation error are very significant due to the selection of different approximation values and orthogonal approximation. In this case, iterative regularization method can be used to solve nonlinear ill-conditioned problems.