猜想：通过对Hilbert矩阵的预处理，能改善Hilbert的病态性质。

验证：根据不同 建立对应的Hilbert矩阵，计算该矩阵的2-范数的条件数，其次计算经过预处理后的H^矩阵的2-范数的条件数，并绘制 曲线。编程实现见附录1中的solution(2)。

实际编程中，分别取 ， ， ， ，可以发现所得到的变化曲线 在 时， 的取值较为平缓的减小，且均小于0。而随着Hilbert矩阵阶数的增大， 的取值在 区间中振荡，主要集中在 ，且多数取值 。则对多数的Hilbert矩阵，其条件数在经过预处理后，有 ，即预处理在一定程度上改善了原Hilbert矩阵的病态性质。

-Conjecture: By Hilbert matrix preconditioning can improve the pathological nature of Hilbert.

Authentication: Depending on the establishment of the corresponding Hilbert matrix, the matrix calculation 2- norm condition number, followed by the calculation 2 after pretreatment of H ^ matrix- norm condition number, and draw the curve. Programming, see Appendix 1 solution (2).

The actual programming, were taken,, can be found in the curve obtained when the value is reduced more gentle and less than 0. With the Hilbert matrix of order increases, the value in the interval oscillations, mainly in, and most of the value. For most of the Hilbert matrix condition number after a pretreatment with, i.e., to some extent, the pretreatment improves the pathological nature of the original Hilbert matrix.