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.)相关搜索： 希尔伯特矩阵
迭代法
正则化方法