The Macaulay2 package PHCpack provides an interface to PHCpack, a generalpurpose polynomial system solver that uses homotopy continuation. The main method is a numerical blackbox solver which is implemented for all Laurent systems. The package also provides a fast mixed volume computation, the ability to filter solutions, homotopy path tracking, and a numerical irreducible decomposition method....

The problem of pricing Bermudan options using Monte Carlo and a nonparametric regression is considered. We derive optimal nonasymptotic bounds for a lower biased estimate based on the suboptimal stopping rule constructed using some estimates of continuation values. These estimates may be of different nature, they may be local or global, with the only requirement being that the deviations of the...

The Macaulay2 package PHCpack provides an interface to PHCpack, a generalpurpose polynomial system solver that uses homotopy continuation. The main method is a numerical blackbox solver which is implemented for all Laurent systems. The package also provides a fast mixed volume computation, the ability to filter solutions, homotopy path tracking, and a numerical irreducible decomposition method....

Numerical homotopy continuation of solutions to polynomial equations is the foundation for numerical algebraic geometry, whose development has been driven by applications of mathematics. We use numerical homotopy continuation to investigate the problem in pure mathematics of determining Galois groups in the Schubert calculus. For example, we show by direct computation that the Galois group of t...

Numerical homotopy continuation of solutions to polynomial equations is the foundation for numerical algebraic geometry, whose development has been driven by applications of mathematics. We use numerical homotopy continuation to investigate the problem in pure mathematics of determining Galois groups in the Schubert calculus. For example, we show by direct computation that the Galois group of t...

Numerical homotopy continuation of solutions to polynomial equations is the foundation for numerical algebraic geometry, whose development has been driven by applications of mathematics. We use numerical homotopy continuation to investigate the problem in pure mathematics of determining Galois groups in the Schubert calculus. For example, we show by direct computation that the Galois group of t...

The forward position kinematics (FPK) of a parallel manipulator with new architecture supposed to be used as a moving mechanism in a flight simulator project is discussed in this paper. The closed form solution for the FPK problem of the manipulator is first determined. It has, then, been shown that there are at most 24 solutions for FPK problem. This result has been verified by using other tec...

Analytic continuation of viscous shock solution for the generalized Burgers equation with polynomial nonlinear source term is investigated. We show that a pertubated wave recovers its analyticity in the space variable in the strip limited by the first pair of conjugate poles of the wave.