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C. J. Tallents, M. D. J. Burgess and B. Luther-Davies, “The Determination of Electron Density Profiles from Re- fraction Measurements Obtained Using Holographic In- terferometry,” Optics Communications, Vol. 44, No. 6, 1983, pp. 384-387. doi:10.1016/0030-4018(83)90222-5

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• TITLE: Solution of the Generalized Abel Integral Equation by Using Almost Bernstein Operational Matrix

  AUTHORS: Sandeep Dixit, Rajesh K. Pandey, Sunil Kumar, Om P. Singh

  KEYWORDS: Abel Inversion, Bernstein Polynomials, Almost Bernstein Operational Matrix Of Integration, Noise Resistance

  JOURNAL NAME: American Journal of Computational Mathematics, Vol.1 No.4, December 9, 2011

  ABSTRACT: A direct almost Bernstein operational matrix of integration is used to propose a stable algorithm for numerical inversion of the generalized Abel integral equation. The applicability of the earlier proposed methods was restricted to the numerical inversion of a part of the generalized Abel integral equation. The method is quite accurate and stable as illustrated by applying it to intensity data with and without random noise to invert and compare it with the known analytical inverse. Thus it is a good method for applying to experimental intensities distorted by noise.