基于随机矩阵的差分代换算法的完备化

Completion of Difference Substitution Method Based on Stochastic Matrix

本文利用有限核原理,给出了基于随机矩阵的逐次差分代换方法的一个完备化.获得了判定多项式半正定性的完全算法.此算法可进一步应用于计算有理函数的全局最优值.与常用的数值最优化方法不同的是,本方法获得的是精确符号解.

In this paper,the principle of finite kernel is used to complete the successive difference substitution.Then a complete algorithm for deciding positive semi-definite polynomial is presented.This algorithm can be applied further to compute the global optimization of rational function.Being different from any other common methods of numerical optimization,the method in this paper gets accurate symbolic solution.