"On growth of
Lebesgue constants in Newton interpolation"

By

**ALEXANDER GONCHAROV**

**(Bilkent University)
**

Abstract: Let *X* be an
infinite triangular array of nodes in [–1,1]. Let L_{n}(*X*) denote
the *n*–th Lebesgue constant, that is the uniform norm of the Lagrange
interpolating operator defined by (*n*
+ 1) – st row of *X*.
It is well-known that the sequence (L_{n} (*X*))_{ }has
at least logarithmic growth and that the Chebyshev
array_{ }*T* is close to the
optimal choice. The problem of growth of the Lebesgue
constants for a monotone array *X* is
open. As a good choice of the sequence that gives the optimal monotone array,
one can suggest the nested family of zeros of Chebyshev
polynomials (T_{3}^{n}), or the Leja
sequence, or another sequence approximating the equilibrium distribution. We
give the size of the Lebesgue constants for the first
case.

**Date: ****Thursday, September 21, 2006**

**Time: ****14.40**

**Place: ****Mathematics Seminar Room, SAZ-141**