Integrable discretization and its applications

Using an integrable discretization of the Rayleigh quotient system, a new algorithm for computing the largest eigenvalue is obtained. The Rayleigh quotient system is discretized by our own method (Bull. Kurume Inst. Technol 11 (1987) 1–7), which solves a quadratic differential equation explicitly. The algorithm converges more rapidly than Wilkinsonʹs power method with a shift of the origin.