CAPACITIES AND JACOBI MATRICES

Two modified Jacobi methods for M-matrices

Jacobi matrices

We discuss the relationships among Jacobi matrices, orthogonal polynomials, spectral measure, moments, minors, Gaussian quadrature, resolvents and continued fractions in the simplest setting, namely the finite-dimensional one. The formal structure is essentially the same as that in the infinite-dimensional setting, where it leads into the rich analytic world of orthogonal polynomials on the rea...

Jacobi Sum Matrices

In this article we identify several beautiful properties of Jacobi sums that become evident when these numbers are organized as a matrix and studied via the tools of linear algebra. In the process we reconsider a convention employed in computing Jacobi sum values by illustrating how these properties become less elegant or disappear entirely when the standard definition for Jacobi sums is utiliz...

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...

Seminar on Jacobi Matrices