北京大学学报(自然科学版)

基于差分代换的正半定型判定完备方法

韩京俊   

  1. 北京大学数学科学学院, 北京 100871;
  • 收稿日期:2012-05-20 出版日期:2013-07-20 发布日期:2013-07-20

A Complete Method Based on Successive Difference Substitution Method for Deciding Positive Semi-definiteness of Polynomials

HAN Jingjun   

  1. School of Mathematical Sciences, Peking University, Beijing 100871;
  • Received:2012-05-20 Online:2013-07-20 Published:2013-07-20

摘要: 研究并发展逐次差分代换方法, 得到Rn+上正半定型差分代换次数的一个上界。 由此获得判定Rn+上 正半定型的充要条件。根据此充要条件建立的算法是必定能终止的。同时提出一类新的差分代换矩阵。

关键词: 逐次差分代换, 差分代换次数, 正半定型, 终止性

Abstract: The successive difference substitution method is studied. The author obtains an upper bound for successive difference substitution times of positive semi-definite polynomials on Rn+. A necessary and sufficient criterion for these polynomials is achieved by using this result. The procedure based on the above arguments always terminates. A new kind of successive difference substitution matrices are proposed.

Key words: successive difference substitution, successive difference substitution times, positive semi-definite, termination

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