Pólya方法与逐次差分代换方法

Pólya’s method and the successive difference substitution method

通过检查某些特定型系数的非负性来证明给定型非负性的方法中,最典型的是Pólya方法与基于重心矩阵的逐次差分代换方法(GSDS).本文完整地比较了这两种方法的适用范围,证明了型f如果可使用Pólya方法证明非负性,则GSDS方法也可以,但反之不然.即GSDS方法的适用范围严格大于Pólya方法的适用范围.

There are two most typical methods for proving the non-negativity of a form by checking the non- negativity of some special forms＇ coefficients： PSlya＇s method and the successive difference substitution method based on the barycentric matrix （GSDS）. In this paper, we proved that if a form f can be proven to be non- negative by P61ya＇s method, then it can also be proven to be non-negative by GSDS, but the reverse is not true. In other words, GSDS can be applied to strictly wider scope than P61ya＇s method.