Markov-switching dynamic stochastic general equilibrium (MSDSGE) modeling has become a growing body of literature on economic and policy issues related to structural shifts. This paper develops a general perturbation methodology for constructing high-order approximations to the solutions of...

The Bezout–Dixon resultant method for solving systems of polynomial equations lends itself to various heuristic acceleration techniques, previously reported by the present author, which can be extraordinarily effective. In this paper we will discuss how well these techniques apply to the...

Using methods from computer algebra, especially Gröbner bases, we study the application which maps the mixtures of two Gaussian laws of probability to their six first moments. It is proved that the mapping is injective, and thus that the parameters of the mixture may be recovered from the...

The Apollonius Circle Problem dates to Greek antiquity, circa 250 b.c. Given three circles in the plane, find or construct a circle tangent to all three. This was generalized by replacing some circles with straight lines. Viéte [Canon mathematicus seu Ad triangula cum adpendicibus, Lutetiae:...