利用高斯消元法法求解病态矩阵——hilbert 矩阵的线性方程组。通过条件数分析，找出误差较大的原因。再利用 Jacobi 迭代方法、G-S 迭代方法和 SOR 迭代法做了进一步探究。另外，作为要求之外的，还使用共轭梯度法来求解方程以来进行对比，并利用Tikhonov 正则化的方法改善矩阵的条件数，来减小误差。(The Gauss elimination method is used to solve the linear equations of the ill conditioned matrix - Hilbert matrix. Through the analysis of the condition number, the cause of the large error is found. The Jacobi iterative method, the G-S iteration method and the SOR iteration method are further explored. In addition, as a requirement, the conjugate gradient method is used to solve the equations, and the Tikhonov regularization method is used to improve the condition number of the matrix to reduce the error.)