科研成果详情

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 τ (λi - 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.