Interpolation on the disk

Interpolation on the disk

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Article ID: iaor2014777
Volume: 66
Issue: 1
Start Page Number: 1
End Page Number: 16
Publication Date: May 2014
Journal: Numerical Algorithms
Authors: ,
Keywords: interpolation
Abstract:

Bivariate polynomials defined on the unit disk are used to reconstruct a wavefront from a data sample. We analyze the interpolation problem arising in critical sampling, that is, using a minimal sample. The interpolant is expressed as a linear combination of Zernike polynomials, whose coefficients represent relevant optical features of the wavefront. We study the propagation of errors of the polynomial values and their coefficients, obtaining bounds for the Lebesgue constants and condition numbers. A node distribution leading to low Lebesgue constants and condition numbers for degrees up to 20 is proposed.

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