一种改进的最优步长积分迭代法

本文基于位场向下延拓的最优步长积分迭代法，通过结合当前迭代步骤得到的迭代信息，经过推导得到了一种新的改进的最优步长积分迭代法迭代形式。此种改进迭代法的实质是将最优迭代法的一步迭代分为两步迭代，且每次迭代过程都使用积分迭代法的迭代形式，因此迭代过程中的计算量并没有明显增加，其收敛性同最优步长积分迭代法。理论模型及实测数据的对比试验表明，改进迭代法的收敛速度和延拓精度均优于最优步长积分迭代法、泰勒级数迭代法和导数迭代法。

An improved optimal step-length integral iteration method

We propose in this paper an improved optimal step-length integral iterative method. Based on the optimal integral iteration method for potential field downward continuation, we use the information in the current iterative step of the iteration method to modify the iteration scheme. The essence of this improved iterative method is divided one-step iteration into two-step iterations, and each iterative process uses the same iterative form of the integral iteration method. Therefore, the calculation amount of the improved iterative method is not increased significantly, and the convergence is the same as the optimal iteration method. The comparison analysis of theoretical model and real gravity data shows that the continuation precision of the improved iteration method is more accurate than that of the other methods, such as optimal step-length integral iteration, the Taylor series iteration and the derivative-iteration.