变阻尼共轭梯度算法及其性能分析

为了提高反演的分辨率和计算效率,本文在传统阻尼共轭梯度法的基础上,提出了变阻尼共轭梯度算法.由于在最小二乘线性反演过程中,多数情况下都要计算偏导数矩阵,而偏导数矩阵列向量的长度大小决定了解向量在对应分量方向上前进的快慢,变阻尼共轭梯度算法的提出正是利用了偏导数矩阵的这一特点.从理论上讲,它要优于传统的固定阻尼共轭梯度法.最后通过计算实例证明了该算法计算精度高,稳定性好,收敛速度快.因此采用变阻尼共轭梯度算法进行地球物理反演是切实可行的.

The conjugate gradient algorithm of variational damping and its capability analysis

In order to improve the resolution of inversion and computational efficiency,this paper puts forward the variational damping conjugate gradient method based on the traditional damping conjugate gradient method.During the linear inversion of least square method,it is necessary to compute the partial derivatives matrix in the majority of inversion,the changed damping conjugate gradient method was invented through utilizing partial derivatives matrix's feature that its length of column vectors decides the speed of convergence for the solution vectors in the corresponding directions.For this theory,it is better than the traditional fixed damping conjugate gradient method.At last,the paper verifies that the calculated precision of this method is high,the stability about it is better,and the speed of convergence about it is fast.Therefore it is feasible to be used to the inversion of geophysics.