An algorithm for calculating D-optimal designs for polynomial regression through a fixed point

Optimal designs are required to make efficient statistical experiments. By using canonical moments, in 1980, Studden found Ds-optimal designs for polynomial regression models. On the other hand, integrable systems are dynamical systems whose solutions can be written down concretely. In this paper, polynomial regression models through a fixed point are discussed. In order to calculate D-optimal designs for these models, a useful relationship between canonical moments and discrete integrable systems is introduced. By using canonical moments and discrete integrable systems, a new algorithm for calculating D-optimal designs for these models is proposed.