解非线性反演问题的新策略

本文提出一种解非线性反演问题的新策略。它首先利用贝叶斯反演理论中的ＭＡＰ方法建立非线性反演问题的线性化迭代格式，然后运用模拟退火算法中有关全局收敛的思想来指导迭代的收敛过程。

A new strategy of solving non-linear inverse problem

This paper presents a new strategy to solve non-linear inverse problem. Firstly the MAPmethod in the Bayes theory is used to construct a linearized iterative algorithm. The idea of global convergence in simulated annealing algorithm is applied to guide the convergence process of iteration. Meanwhile the global convergence of iterative solution estimate is further guaranteed by adding random purturbation in solution estimate according to its convergence situation. In conventional linearized iterative inversion methoods, a good initial solution estimate is needed, or else the iteration may easily fall into a pitof locally optimal solution. The new strategy overcomes this drawback, and spends less computationalamount than the simulated annealing algorithm. It is adaptive specially to the non-linear inverse problemwith little priori information.The effect of linearized error on iterative solution estimate is discussed deeply through comparing theinversion strategy with the non-linear damped least-square methed. On the basis of this, the authars putforward viewpoints about the selection of damping factor, the trend of iterative solution estimate, andthe locally optimal solution estimation.