Interpolation on the disk (Q2453468)

In this paper the authors use bivariate polynomials defined on the unit disk to construct a wavefront from a data sample. They consider the polynomial interpolation problem corresponding to critical sampling and analyse the stability of a solution and the propagation of errors through the introduction of condition numbers and Lebesgue constants. The interpolant is expressed as a linear combination of Zernike polynomials, whose coefficients represent relevant optical features of the wavefront.