Stability properties of disk polynomials


Disk polynomials form a basis of orthogonal polynomials on the disk corresponding to the radial weight \({\alpha +1 \over \pi }(1-r^{2})^{\alpha }\). In this paper, the stability properties of disk polynomials are analyzed. A conditioning associated with the representation of the least squares approximation with respect to this basis is introduced and bounded. Among all disk polynomials, the least bounds are obtained for Zernike polynomials corresponding to α = 0.

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This work has been partially supported by the PGC2018-096321-B-I00 Spanish Research Grant, by Gobierno de Aragó n E41_17R and Feder 2014-2020 “Construyendo Europa desde Aragón”.

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Correspondence to E. Mainar.

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Carnicer, J.M., Mainar, E. & Peña, J.M. Stability properties of disk polynomials. Numer Algor (2020).

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  • Orthogonal polynomials
  • Disk polynomials
  • Zernike polynomials
  • Lebesgue constant
  • conditioning

Mathematics Subject Classification (2010)

  • 41A10
  • 41A63
  • 33C50
  • 65F35