The Characteristic Function for Complex Doubly Infinite Jacobi Matrices

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...

On the determinacy of complex Jacobi matrices

The aim of this paper is to explore to which extend the theory of the Hamburger moment problem for real Jacobi matrices generalizes to the case of complex Jacobi matrices. In particular, we characterize the indeterminacy in terms of uniqueness of closed extensions of Jacobi matrices, and discuss the link to the growth of the smallest singular values of the underlying Hankel matrices. As a bypro...

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.

DETERMINACY OF COMPLEX JACOBI MATRICES 21 Introdu