Asymptotics of the discrete spectrum for complex Jacobi matrices

The Discrete Spectrum for Complex Perturbations of Periodic Jacobi Matrices

We study spectrum inclusion regions for complex Jacobi matrices which are compact perturbations of real periodic Jacobi matrix. The condition sufficient for the lack of discrete spectrum for such matrices is given.

On the location of the discrete spectrum for complex Jacobi matrices

We study spectrum inclusion regions for complex Jacobi matrices that are compact perturbations of the discrete laplacian. The condition sufficient for the lack of discrete spectrum for such matrices is given.

On Limit Sets for the Discrete Spectrum of Complex Jacobi Matrices

The discrete spectrum of complex Jacobi matrices that are compact perturbations of the discrete laplacian is under consideration. The rate of stabilization for the matrix entries sharp in the sense of order which provides finiteness of the discrete spectrum is found. The Jacobi matrix with the discrete spectrum having the only limit point is constructed. The results can be viewed as the discret...

Two modified Jacobi methods for M-matrices

Complex Jacobi Matrices

Complex Jacobi matrices play an important role in the study of asymptotics and zero distribution of Formal Orthogonal Polynomials (FOPs). The latter are essential tools in several elds of Numerical Analysis, for instance in the context of iterative methods for solving large systems of linear equations, or in the study of Pad e approximation and Jacobi continued fractions. In this paper we prese...