大型广义逆反演中求逆算法的比较

Comparison of Iterative Method for Large Generalized Inverse Algorithm

目前地球物理反演中应用最广泛、最重要的一类反演方法就是广义反演。由于地球物理反演中的数据量大、模型参数多,所以在对一个反演问题建立模型方程后就要寻求一种合适高效的算法来处理它。本文首先介绍现有几种迭代求逆的方法,然后通过Matlab设计的大型高条件数矩阵,比较了共轭梯度法以及两种基于预条件算子的迭代算法,结果表明共轭梯度法迭代方法对于条件数巨大的矩阵解算效率很低,而基于预条件算子的迭代算法具有明显的优势。

Generalized inverse is one of the most popular ways in geophysics. Because of the large amount of data and model parameters in geophysics, more effective algorithm should be found out to solve matrix equation. Firstly, the authors of lhis paper will introduce some iterative methods for inverse such as Conjugate Gradient （CG）, and then, design some matrices which are sparse, symmetric, large condition number by Matlab to demonstrate the efficiency of individual iteration method. Finally, a comparison between common CG method and the preconditioning CG ones which is based on the incomplete factorization on the designated matrices is made. The result indicates that the lat- ter has better performance in convergence, speed and process time than the former, and the preconditioning with Cholesky factorization has the best efficiency.