By viewing the operations of the Richardson purification algorithm as a discrete time dynamical process, we propose a method to overcome the instability of the algorithm by controlling chaos. We present theoretical analysis and numerical results on the behavior and performance of the stabilized algorithm. Typeset using REVTEX

We revisit an algorithm by Skeel et al. [5, 16] for computing the modified, or shadow, energy associated with symplectic discretizations of Hamiltonian systems. We amend the algorithm to use Richardson extrapolation in order to obtain arbitrarily high order of accuracy. Error estimates show that the new method captures the exponentially small drift associated with such discretizations. Several ...

We prove that a conjecture of Fomin, Fulton, Li, and Poon, associated to ordered pairs of partitions, holds for many infinite families of such pairs. We also show that the bounded height case can be reduced to checking that the conjecture holds for a finite number of pairs, for any given height. Moreover, we propose a natural generalization of the conjecture to the case of skew shapes.