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Interpolation on the disk

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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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Authors and Affiliations

  1. Departamento de Matemática Aplicada/IUMA, Universidad de Zaragoza, Zaragoza, Spain

    J. M. Carnicer & C. Godés

Authors
  1. J. M. Carnicer
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  2. C. Godés
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Correspondence to J. M. Carnicer.

Additional information

Partially supported by the Spanish Research Grant MTM2012-31544 and by Gobierno de Aragón and Fondo Social Europeo

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Carnicer, J.M., Godés, C. Interpolation on the disk. Numer Algor 66, 1–16 (2014). https://doi.org/10.1007/s11075-013-9720-0

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  • DOI: https://doi.org/10.1007/s11075-013-9720-0

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