"On growth of Lebesgue constants in Newton interpolation"
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.
Place: Mathematics Seminar Room, SAZ-141