Jean-Paul Calvi

Uniform approximation by discrete least squares polynomials

We study uniform approximation of differentiable or analytic functions of one or several variables on a compact set K by a sequence of discrete least squares polynomials. In particular, if K satisfies a Markov inequality and we use point evaluations on standard discretization grids with the number of points growing polynomially in the degree, these polynomials provide nearly optimal approximants. For analytic functions, similar results may be achieved on more general K by allowing the number of points to grow at a slightly larger rate.

Full length articles: On the Lebesgue constant of Leja sequences for the unit disk and its applications to multivariate interpolation

We estimate the growth of the Lebesgue constant of any Leja sequence for the unit disk. The main application is the construction of new multivariate interpolation points in a polydisk (and in the Cartesian product of many plane compact sets) whose Lebesgue constant grows (at most) like a polynomial.We show that the Lebesgue constant of the real projection of Leja sequences for the unit disk grows like a polynomial. The main application is the first construction of explicit multivariate interpolation points in

Kergin interpolants at the roots of unity approximate C2 functions

[-1,1]^N

Intertwining unisolvent arrays for multivariate Lagrange interpolation

whose Lebesgue constant also grows like a polynomial.

On the Siciak extremal function for real compact convex sets

AbstractWe establish a new formula for Kergin interpolation in the plane and use it to prove that the Kergin interpolation polynomials at the roots of unity of a function of classC2 in a neighborhood of the unit disc

Interpolation in Fréchet spaces with an application to complex function theory

{\mathbb{D}}

Mikael Passare, a Jaunt in Approximation Theory

converge uniformly to the function on