Description: 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.
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