"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 Ln(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 (Ln (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 (T3n), or the Leja
sequence, or another sequence approximating the equilibrium distribution. We
give the size of the Lebesgue constants for the first
case.
Date:
Time: 14.40
Place: Mathematics Seminar Room, SAZ-141