In this paper we study the problem of description of conjugacy classes in the group SL(n,Z). Gauss Reduction Theory gives the answer for the case n = 2, for n ≥ 3 the problem is still open. We introduce a new approach to this problem based on reduction to reduced Hessenberg matrices. An important tool used in our approach is to determine minima of Markoff-Davenport characteristics at the vertic...

We introduce in this paper a method to calcúlate the Hessenberg matrix of a sum of measures from the Hessenberg matrices of the component measures. Our method extends the spectral techniques used by G. Mantica to calcúlate the Jacobi matrix associated with a sum of measures from the Jacobi matrices of each of the measures. We apply this method to approximate the Hessenberg matrix associated wit...

The implicitly shifted (bulge chasing) QZ algorithm is the most popular method for solving the generalized eigenvalue problem Av = Bv. This paper explains why the QZ algorithm functions well even in the presence of innnite eigenvalues. The key to rapid convergence of QZ (and QR) algorithms is the eeective transmission of shifts during the bulge chase. In this paper the mechanism of transmission...

In this paper, we consider the generalized Fibonacci and Pell Sequences and then show the relationships between the generalized Fibonacci and Pell sequences, and the Hessenberg permanents and determinants. 1. Introduction The Fibonacci sequence, fFng ; is de…ned by the recurrence relation, for n 1 Fn+1 = Fn + Fn 1 (1.1) where F0 = 0; F1 = 1: The Pell Sequence, fPng ; is de…ned by the recurrence...