Statistics – Applications
Scientific paper
Jun 1978
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1978jimia..21..429h&link_type=abstract
Institute of Mathematics and Its Applications, Journal, vol. 21, June 1978, p. 429-443.
Statistics
Applications
Fredholm Equations, Least Squares Method, Limb Darkening, Solar Limb, Spline Functions, Cubic Equations, Random Noise
Scientific paper
A nonlinear least squares method is described for the inversion of the solar limb-darkening equation, a Fredholm integral equation of the first kind. The unknown function in the integrand is approximated by a spline function with variable knots to be determined by the inversion. Representation of this spline in terms of a basis of B-splines provides a convenient and effective approach to the inversion. The method is demonstrated in a numerical experiment using cubic splines and synthetic solar data with and without the addition of pseudo-random noise, and appears to be quite stable. A comparison with fixed knot inversions is also described. The method has the property of providing an estimate of the important model parameters at the solution, and is applicable in principle to other integral equations of the first kind.
Holt J. N.
Jupp David L. B.
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