New eigenvalue estimates for complex matrices

Eigenvalue Estimates for Preconditioned Saddle Point Matrices

New eigenvalue bounds for symmetric matrices of saddle point form are derived and applied for preconditioned versions of the matrices. The preconditioners enable efficient iterative solution of the corresponding linear systems with, for some important applications, an optimal order of computational complexity.

Ela an Eigenvalue Inequality and Spectrum Localization for Complex Matrices∗

Using the notions of the numerical range, Schur complement and unitary equivalence, an eigenvalue inequality is obtained for a general complex matrix, giving rise to a region in the complex plane that contains its spectrum. This region is determined by a curve, generalizing and improving classical eigenvalue bounds obtained by the Hermitian and skew-Hermitian parts, as well as the numerical ran...

An eigenvalue inequality and spectrum localization for complex matrices

Using the notions of the numerical range, Schur complement and unitary equivalence, an eigenvalue inequality is obtained for a general complex matrix, giving rise to a region in the complex plane that contains its spectrum. This region is determined by a curve, generalizing and improving classical eigenvalue bounds obtained by the Hermitian and skew-Hermitian parts, as well as the numerical ran...

Eigenvalue Estimates for Schrödinger Operators with Complex Potentials

Throughout the paper, f± denotes either the positive or the negative part of f , which is, in its turn, either a function or a selfadjoint operator. The symbols <z and =z denote the real and the imaginary part of z. Finally, if a is a function on R, then a(i∇) is the operator whose integral kernel is (2π)−d ∫ eiξ(x−y)a(ξ)dξ. We consider the Schrödinger operator H = −∆ + V with a complex potenti...

Several new inequalities for the minimum eigenvalue of M-matrices