大型方程组快速解算方法研究

Research on the Efficient Inversion Methods for a Large Linear System

本文研究了大型方程组的解算方法，给出了改进的共轭梯度算法和预条件共轭梯度算法，推导了相应的计算公式。对各种算法的计算效率进行了比较，结果表明，改进的共轭梯度法和预条件共轭梯度法能有效提高大型方程组的解算效率，其缺点是不能精确给出参数估值的验后协方差矩阵。

The efficient inversion methods for a large linear system are studied in this paper. An improved method of coniugate gradient is presented. The efficiency for the three methods, which is least squares estima tion, conjugate gradient and pre-eonditioned conjugate gradient which are commonly used in gravity field reeo very, are compared. The results show that the improved conjugate gradient method and pre-conditioned coniu gate gradient method can greatly improve the efficiency of inversion for a large linear system, hut they cannot provide the posterior variance-covariance matrix of the estimated parameters.