Relative Perturbation Bounds for Eigenvalues of Symmetric Positive Definite Diagonally Dominant Matrices

This paper presents a linear and quadratic residual bound for eigenvalues of an indefinite possible singular Hermitian matrix. These bounds are a generalization of results on a semidefinite Hermitian matrix [Z. Drmacˇ and V. Hari, SIAM J. Matrix Anal. ...

We show that three well-known perturbation bounds for matrix eigenvalues imply relative bounds: the Bauer--Fike and Hoffman--Wielandt theorems for diagonalizable matrices, and Weyl's theorem for Hermitian matrices. As a consequence, relative ...

This paper proves that the two-sided Jacobi method computes the eigenvalues of the indefinite symmetric matrix to high relative accuracy, provided that the initial matrix is scaled diagonally dominant. It proves sharp eigenvalue perturbation bounds ...