Combined perturbation bounds : I. Eigensystems and singular value decompositions

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)643-655
Journal / PublicationSIAM Journal on Matrix Analysis and Applications
Issue number2
Publication statusPublished - 2007


In this paper we present some new combined perturbation bounds of eigenvalues and eigensubspaces for a Hermitian matrix H, particularly in an asymptotic sense, δ122|| sin Θ (U1, Ũ1)||F2 + Σi=1 τi - λ̃i)2 ≤ || ΔHU1||F2 + O (||ΔHU 1||F4), where λi denotes the eigenvalues of H and U1 the eigensubspace corresponding to the eigenvalues λi, i = 1, 2, . . . , r. The bound for each factor of eigensystems is optimal due to the sine theorem and the Hoffman-Wielandt theorem. In addition, combined perturbation bounds for singular value decompositions and combined perturbation bounds in some, more general, measures are also obtained. © 2007 Society for Industrial and Applied Mathematics.

Research Area(s)

  • Combined perturbation bound, Eigensystems, Singular subspace, Singular value