中文摘要：

提出了病态代数系统求解的精细迭代方法．首先利用一个小参数对病态矩阵加以改良，将原病态系统的求解问题转化为该改良系统的求解问题．然后利用精细积分法给出了改良矩阵求逆的高精度方法．该方法具有高精度、高效率的优点，且对改良参数的适应性较好，具有良好的应用前景．理论和数值分析证明了该方法的有效性．

英文摘要：

A precise iterative refinement of solution for ill-conditioned systems of linear alge- braic equations was proposed. First, the ill-conditioned matrix was improved through introduc- tion of a small parameter, and then via the precise integration method, a highly precise method was provided for the inversion of the improved matrix. Both the theoretical convergence analy- sis and numerical examples show the efficiency and accuracy of the method.