Inversion of Abel’s Integral Equation by Means of Orthogonal Polynomials
1969; Society for Industrial and Applied Mathematics; Volume: 6; Issue: 4 Linguagem: Inglês
10.1137/0706055
ISSN1095-7170
Autores Tópico(s)Near-Field Optical Microscopy
ResumoPrevious article Inversion of Abel’s Integral Equation by Means of Orthogonal PolynomialsGerald N. Minerbo and Maurice E. LevyGerald N. Minerbo and Maurice E. Levyhttps://doi.org/10.1137/0706055PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] O. H. Nestor and , H. N. Olsen, Numerical methods for reducing line and surface probe data, SIAM Rev., 2 (1960), 200–207 10.1137/1002042 MR0119435 0090.34504 LinkISIGoogle Scholar[2] Mark P. Freeman and , S. Katz, Determination of the radial distribution of brightness in a cylindrical luminous medium with self-absorption, J. Opt. Soc. Amer., 50 (1960), 826–830 MR0119436 CrossrefISIGoogle Scholar[3] K. Bockasten, Transformation of observed radiances into radial distribution of the emission of a plasma, J. Opt. Soc. Amer., 51 (1961), 943–947 CrossrefISIGoogle Scholar[4] W. L. Barr, Method for computing the radial distribution of emitters in a cylindrical source, J. Opt. Soc. 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Rank, 1965, Note 727, Davidson Laboratory, Stevens Institute of Technology, Hoboken, New Jersey Google Scholar Previous article FiguresRelatedReferencesCited byDetails Physics of plasmas confined by a dipole magnet: insights from compact experiments driven at steady state12 July 2022 | Reviews of Modern Plasma Physics, Vol. 6, No. 1 Cross Ref WEST tokamak hard x-ray tomography inversionAIP Advances, Vol. 11, No. 8 Cross Ref Characterizing spatially varying optical emissions in a steady-state dipole plasma: inversion based experiments and modeling25 January 2021 | Physica Scripta, Vol. 96, No. 3 Cross Ref Intrinsic Properties of Strongly Continuous Fractional Semigroups in Normed Vector Spaces11 May 2021 Cross Ref Characterization of Engine Combustion Flames Using Inverse Abel Transform19 August 2020 Cross Ref GNSS Radio Occultation15 December 2020 Cross Ref An efficient and stable Lagrangian matrix approach to Abel integral and integro-differential equationsApplied Mathematics and Computation, Vol. 374 Cross Ref A singularity free and derivative free approach for Abel integral equation in analyzing the laser-induced breakdown spectroscopySpectrochimica Acta Part B: Atomic Spectroscopy, Vol. 167 Cross Ref AVIATOR: Morphological object reconstruction in 3D22 January 2020 | Astronomy & Astrophysics, Vol. 633 Cross Ref Solutions of the Generalized Abel’s Integral Equations of the Second Kind with Variable Coefficients5 December 2019 | Axioms, Vol. 8, No. 4 Cross Ref New Stable Numerical Inversion of Generalized Abel Integral Equation7 August 2018 Cross Ref Numerical Schemes for the Generalized Abel’s Integral Equations7 March 2018 | International Journal of Applied and Computational Mathematics, Vol. 4, No. 2 Cross Ref Babenko’s Approach to Abel’s Integral Equations1 March 2018 | Mathematics, Vol. 6, No. 3 Cross Ref A new operational method to solve Abel’s and generalized Abel’s integral equationsApplied Mathematics and Computation, Vol. 317 Cross Ref A fast algorithm for the inversion of Abel’s transformApplied Mathematics and Computation, Vol. 301 Cross Ref Applications of fractional calculus in solving Abel-type integral equations: Surface–volume reaction problemComputers & Mathematics with Applications, Vol. 73, No. 6 Cross Ref Generalized quadrature for solving singular integral equations of Abel type in application to infrared tomographyApplied Numerical Mathematics, Vol. 106 Cross Ref Direct and inverse problems of infrared tomography24 December 2015 | Applied Optics, Vol. 55, No. 1 Cross Ref An approximate method for Abel inversion using Chebyshev polynomialsApplied Mathematics and Computation, Vol. 237 Cross Ref On the Decay of the Elements of Inverse Triangular Toeplitz MatricesNeville J. 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