Relative perturbation results for eigenvalues and eigenvectors of diagonalisable matrices期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

Relative perturbation results for eigenvalues and eigenvectors of diagonalisable matrices

Authors:	S C Eisenstat I C F Ipsen

Institution:	(1) Department of Computer Science, Yale University, P.O. Box 208285, 06520-8285 New Haven, CT, USA;(2) Department of Mathematics, North Carolina State University, P.O. Box 8205, 27695-8205 Raleigh, NC, USA

Abstract:	Let $\hat \lambda$ and $\hat x$ be a perturbed eigenpair of a diagonalisable matrixA. The problem is to bound the error in $\hat \lambda$ and $\hat \lambda$ . We present one absolute perturbation bound and two relative perturbation bounds. The absolute perturbation bound is an extension of Davis and Kahan's sin θ Theorem from Hermitian to diagonalisable matrices. The two relative perturbation bounds assume that $\hat \lambda$ and $\hat x$ are an exact eigenpair of a perturbed matrixD ₁ AD ₂, whereD ₁ andD ₂ are non-singular, butD ₁ AD ₂ is not necessarily diagonalisable. We derive a bound on the relative error in $\hat \lambda$ and a sin θ theorem based on a relative eigenvalue separation. The perturbation bounds contain both the deviation ofD ₁ andD ₂ from similarity and the deviation ofD ₂ from identity. This work was partially supported by NSF grant CCR-9400921.

Keywords:	15A18 15A42 15A60 65F15 65F35 65G99
本文献已被 SpringerLink 等数据库收录！