Origin-shifted algorithm for matrix eigenvalues

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	Origin-shifted algorithm for matrix eigenvalues
	Nie YY(聂义勇); Li, Z.; Han JD(韩建达)
刊名	INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
	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
内容类型	期刊论文
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.