Short note: An integrable numerical algorithm for computing eigenvalues of a specially structured matrix

This paper is motivated by some recent work of Fukuda, Ishiwata, Iwasaki, and Nakamura (Inverse Problems 2009; 25:015007). We first design an algorithm for computing the eigenvalues of a specially structured matrix from the discrete Bogoyavlensky Lattice 2 (dBL2) system. A Lax representation for the dBL2 system is given in a matrix form. By considering the asymptotic behavior of dBL2 variables, some characteristic polynomials are then factorized. A new algorithm for computing the complex eigenvalues of a specially structured matrix is then introduced. Copyright © 2010 John Wiley & Sons, Ltd.