The study of Jacobi and cyclic Jacobi matrix eigenvalue problems using Sturm-Liouville theory

We study the eigenvalues of matrix problems involving Jacobi and cyclic Jacobi matrices as functions of certain entries. Of particular interest are the limits of the eigenvalues as these entries approach infinity. Our approach is to use the recently discovered equivalence between these problems and a class of Sturm-Liouville problems and then to apply the Sturm-Liouville theory.