The characteristic function for Jacobi matrices with applications

Two modified Jacobi methods for M-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...

The Szego condition for Coulomb Jacobi matrices

A Jacobi matrix with an → 1, bn → 0 and spectral measure ν(x)dx + dνsing(x) satisfies the Szegő condition if

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...