| 引用本文: | 刘永清,韩京清,金维言,秦元勋.代数方程的根具有负实部的判定[J].控制理论与应用,1987,4(4):41~47.[点击复制] |
| Liu Yongqing, Han Jingqing, Jin Weiyan, Chin Yuanshun.ON THE CRITERION FOR ALL ROOTS OF THE POLYNOMIAL EQUATION POSSESSING NEGATIVE REAL PARTS[J].Control Theory & Applications,1987,4(4):41~47.[点击复制] |
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| 代数方程的根具有负实部的判定 |
| ON THE CRITERION FOR ALL ROOTS OF THE POLYNOMIAL EQUATION POSSESSING NEGATIVE REAL PARTS |
| 摘要点击 1612 全文点击 573 投稿时间：1985-12-31 修订日期：1986-07-17 |
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| DOI编号 |
| 1987,4(4):41-47 |
| 中文关键词 |
| 英文关键词 |
| 基金项目 |
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| 中文摘要 |
| 本文给出了代数方程f(x)=a0xn+a1xn-1+…+ an-1x+an=0的全部根具有负实部可由不等式：a1a2>pnq1a0a3, a2a3>pnq2a1a4, …, an-2an-1>pnqn-2an-3an来确定，证明了pn的存在性和唯一性，以及最小可取数pn*的存在性唯一性。并对n<=8给出了pn的数值估计。 |
| 英文摘要 |
| In this paper, it is proved that all roots of the polynomial equation a0xn+a1xn-1+…+ an-1x+an=0 have negative real parts if the following inequalities hold: a1a2>pnq1a0a3, a2a3>pnq2a1a4, …, an-2an-1>pnqn-2an-3an. The existence and the uniqueness of the real pn are proved also. At the same time, the existence and uniqueness of the most minimum numbers pn* which can be chose are obtained. The estimated formula real pn for n<=8 are obtained. |
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