Monotone discrete Newton iterations and elimination

Monotone Iterations for Eliptic Variational Inequalities

Monotone Iterations for Elliptic Variational Inequalities

A wide range of free boundary problems occurring in engineering and industry can be rewritten as a minimization problem for a strictly convex, piecewise smooth but non–differentiable energy functional. The fast solution of related discretized problems is a very delicate question, because usual Newton techniques cannot be applied. We propose a new approach based on convex minimization and constr...

On discrete a-unimodal and a-monotone distributions

Unimodality is one of the building structures of distributions that like skewness, kurtosis and symmetry is visible in the shape of a function. Comparing two different distributions, can be a very difficult task. But if both the distributions are of the same types, for example both are unimodal, for comparison we may just compare the modes, dispersions and skewness. So, the concept of unimodali...

Elimination Theory and Newton Polytopes

Algorithms for combinatorial structures: Well-founded systems and Newton iterations

We consider systems of recursively defined combinatorial structures. We give algorithms checking that these systems are well founded, computing generating series and providing numerical values. Our framework is an articulation of the constructible classes of Flajolet & Sedgewick with Joyal’s species theory. We extend the implicit species theorem to structures of size zero. A quadratic iterative...