Origin-shifted algorithm for matrix eigenvalues
文献类型：期刊论文
| 作者 | Nie YY(聂义勇); Li, Z.; Han JD(韩建达)
|
| 刊名 | INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
 |
| 出版日期 | 2008 |
| 卷号 | 85期号:9页码:1397-1411 |
| 关键词 | matrix eigenvalues origin shifts Hessenberg matrix Frobenius-like form quasi-Routh array |
| ISSN号 | 0020-7160 |
| 产权排序 | 1 |
| 中文摘要 | In this paper an origin-shifted algorithm for matrix eigenvalues based on Frobenius-like form of matrix and the quasi-Routh array for polynomial stability is given. First, using Householder's transformations, a general matrix A is reduced to upper Hessenberg form. Secondly, with scaling strategy, the origin-shifted Hessenberg matrices are reduced to the Frobenius-like forms. Thirdly, using quasi-Routh array, the Frobenius-like matrices are determined whether they are stable. Finally, we get the approximate eigenvalues of A with the largest real-part. All the eigenvalues of A are obtained with matrix deflation. The algorithm is numerically stable. In the algorithm, we describe the errors of eigenvalues using two quantities, shifted-accuracy and satisfactory-threshold. The results of numerical tests compared with QR algorithm show that the origin-shifted algorithm is fiducial and efficient for all the eigenvalues of general matrix or for all the roots of polynomial. |
| WOS标题词 | Science & Technology ; Physical Sciences |
| 类目[WOS] | Mathematics, Applied |
| 研究领域[WOS] | Mathematics |
| 关键词[WOS] | POLYNOMIAL STABILITY ; QR TRANSFORMATION ; CRITERIA |
| 收录类别 | SCI |
| 语种 | 英语 |
| WOS记录号 | WOS:000258626300008 |
| 公开日期 | 2012-05-29 |
| 源URL | [http://ir.sia.cn/handle/173321/7389]  |
| 专题 | 沈阳自动化研究所_机器人学研究室 |
| 推荐引用方式 GB/T 7714 | Nie YY,Li, Z.,Han JD. Origin-shifted algorithm for matrix eigenvalues[J]. INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS,2008,85(9):1397-1411. |
| APA | Nie YY,Li, Z.,&Han JD.(2008).Origin-shifted algorithm for matrix eigenvalues.INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS,85(9),1397-1411. |
| MLA | Nie YY,et al."Origin-shifted algorithm for matrix eigenvalues".INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 85.9(2008):1397-1411. |
入库方式： OAI收割
来源：沈阳自动化研究所
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