基于列随机矩阵的逐次差分代换与正半定型的机械化判定

本文选择列随机平均矩阵T_n作为基本代换矩阵,建立了基于T_n的逐次差分代换方法.获得了R_+~n上正半定型,不定型判定的充要条件.并进一步证明了:正定型的差分代换集序列正向终止.根据这些结果编写的Maple程序TSDS3,能够自动证明代数型不等式,对不成立的不等式总能输出反例.该程序虽可能不停机,但大量的应用实例证实了该方法的实用性.

Infinite product convergence of column stochastic mean matrix and machine decision for positive semi-definite forms

First we define the column stochastic mean matrix, and then prove that if we choose countable infinite matrices from finite n x n column stochastic mean ones at random （repeats allowed）, then the product of these infinite matrices will converge to a column stochastic mean matrix with rank 1. Finally we show the proof for relations between the termination of the sequence of SDS sets and positive semi-definite property of a form. This method is verified to be very efficient and better than Polya method.