On the poisedness of Bojanov-Xu interpolation

Erratum: On a Hermite interpolation by polynomials of two variables

On polynomial interpolation of two variables

On Polynomial Interpolation on the Unit Ball

Polynomial interpolation on the unit ball of R d has a unique solution if the points are located on several spheres inside the ball and the points on each sphere solves the corresponding interpolation problem on the sphere. Furthermore, the solution can be computed in a recursive way.

On minimal cubature formulae for product weight functions 1

We derive in a simple way certain minimal cubature formulae, obtained by Morrow and Patterson [2], and Xu [4], using a different technique. We also obtain in explicit form new near minimal cubature formulae. Then, as a corollary, we get a compact expression for the bivariate Lagrange interpolation polynomials, based on the nodes of the cubature.

Self-Correcting Geometry in Model-Based Algorithms for Derivative-Free Unconstrained Optimization

Several efficient methods for derivative-free optimization (DFO) are based on the construction and maintenance of an interpolation model for the objective function. Most of these algorithms use special “geometry-improving” iterations, where the geometry (poisedness) of the underlying interpolation set is made better at the cost of one or more function evaluations. We show that such geometry imp...