Discrete Integrable Systems of Hungry Type and Numerical Algorithms for Eigenvalues of Nonsymmetric Matrices : Recent Developments in Integrable Algorithms(Survey,<Special Topics>Activity Group "Applied Integrable Systems")

Abstract

Some numerical algorithms for computing eigenvalues of nonsymmetric matrix with high accuracy have been recently designed based on the discrete hungry Toda equation and the discrete Lotka-Volterra system which are known as the discrete integrable systems of hungry type. In this paper, not only the process for formulating these algorithms but also the results concerning asymptotic analysis through the center manifold theory, mixed error analysis in floating point arithmetic and shift of origin for accelerating convergence are shortly explained. Backlund transformations between discrete integrable systems of hungry type are also shown.