| 基于差分代换的正半定型判定完备方法 |
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| 引用本文： | 韩京俊. 基于差分代换的正半定型判定完备方法[J]. 北京大学学报(自然科学版), 2013, 49(4): 545 |
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| 作者姓名： | 韩京俊 |
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| 作者单位： | 北京大学数学科学学院, 北京 100871; |
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| 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。
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| 关 键 词： | 逐次差分代换 差分代换次数 正半定型 终止性 |
| 收稿时间： | 2012-05-20 |
A Complete Method Based on Successive Difference Substitution Method for Deciding Positive Semi-definiteness of Polynomials |
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| HAN Jingjun. A Complete Method Based on Successive Difference Substitution Method for Deciding Positive Semi-definiteness of Polynomials[J]. Acta Scientiarum Naturalium Universitatis Pekinensis, 2013, 49(4): 545 |
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| Authors: | HAN Jingjun |
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| Affiliation: | School of Mathematical Sciences, Peking University, Beijing 100871; |
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| 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. |
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| Keywords: | successive difference substitution successive difference substitution times positive semi-definite termination |
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