A Numerical Method for Constructing Isospectral Discrete Systems

摘要

Isospectral systems have identical spectra. The problem of finding discrete systems isospectral to a given one, is posed as a problem of finding roots of a nonlinear error function, and solved using the secant method. Horn's majorization theorem and the Gershgorin disk theorem are applied to generate good initial points for the secant method. Secant method with different starting points converge to multiple roots of the error function, generating multiple isospectral systems. The numerical approach used in this paper has widespread applications in dynamics and also has pedagogical applications in courses on numerical analysis and mechanics.