论文信息 - A relative perturbation bound for positive definite matrices - 字舞流文

A relative perturbation bound for positive definite matrices

Abstract We give a sharp estimate for the eigenvectors of a positive definite Hermitian matrix under a floating-point perturbation. The proof is elementary.

Roy Mathias | Krešimir Veselić

[1] Ilse C. F. Ipsen,et al. Relative perturbation techniques for singular value problems , 1995 .

[2] J. Barlow,et al. Computing accurate eigensystems of scaled diagonally dominant matrices: LAPACK working note No. 7 , 1988 .

[3] James Demmel,et al. Jacobi's Method is More Accurate than QR , 1989, SIAM J. Matrix Anal. Appl..

[4] Ivan Slapničar,et al. Floating-point perturbations of Hermitian matrices , 1993 .

[5] A. Sluis. Condition numbers and equilibration of matrices , 1969 .

[6] John G. Lewis,et al. Proceedings of the Fifth SIAM Conference on Applied Linear Algebra , 1994 .

[7] Ren-Cang Li,et al. Relative Perturbation Theory: II. Eigenspace and Singular Subspace Variations , 1996, SIAM J. Matrix Anal. Appl..

[8] Ivan Slapničar,et al. Perturbations of the eigenprojections of a factorized Hermitian matrix , 1995 .