| 引用本文: | 胡庆军.判断实对称矩阵为正定、半正定、负定、半负定或不定的一个算法.[J].国防科技大学学报,1996,18(3):142-146 ，156.[点击复制] |
| Hu Qingjun.A Algorithm for Distinguishing a Real Symmetric Matrix into a Positive（Semi-) Definite，Negative（Semi-) Definite or Non-definite Matrix[J].Journal of National University of Defense Technology,1996,18(3):142-146 ，156[点击复制] |
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| 判断实对称矩阵为正定、半正定、负定、半负定或不定的一个算法 |
| 胡庆军 |
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(国防科技大学 系统工程与数学系 湖南 长沙 410073)
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| 摘要: |
| 给出判别实对称矩阵为正定、半正定、负定、半负定或不定的一个算法;采用选最大对角元的方法，可使数值计算稳定性好。讨论了该算法的运算量，得到乘除法和加减法总次数分别至多为n(n-1)(n+4)/6和n(n-1)(n+1)/6 的结论。最后给出运行该算法的数值例子。 |
| 关键词: 实对称矩阵，类型，判别算法，运算量 |
| DOI： |
| 投稿日期：1996-01-13 |
| 基金项目: |
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| A Algorithm for Distinguishing a Real Symmetric Matrix into a Positive（Semi-) Definite，Negative（Semi-) Definite or Non-definite Matrix |
| Hu Qingjun |
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(Department of Systems Engineering and Mathematics，NUDT，Changsha，410073)
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| Abstract: |
| This paper presents a algorithm for distinguishing a real symmetric matrix into a positive definite, positive semidefinite, negative definite ,negative semidefinite or non-definite matrix. With the technique of selecting maximum diagonal element，the stability of numerical computation for the algorithm is good. The operation numbers of the algorithm is given and the total number of operations of multiplication or division and addition or subtraction of the algorithm are, respectively,at most 1/6 n (n-1)(n+4) and 1/6 n (n-1)(n+1). The numerical examples are given. |
| Keywords: real symmetric matrix,type,distinguishing algorithm,operation numbers |
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