Astronomy and Astrophysics – Astrophysics
Scientific paper
Nov 1992
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1992a%26a...265..289t&link_type=abstract
Astronomy and Astrophysics (ISSN 0004-6361), vol. 265, no. 1, p. 289-295.
Astronomy and Astrophysics
Astrophysics
5
Bayes Theorem, Solar Interior, Solar Oscillations, Solar Rotation, Data Smoothing, Least Squares Method
Scientific paper
The problem of obtaining the solar rotation as a function of radius from splittings in solar oscillations by quadratic regularization is addressed. An efficient method is derived for obtaining smooth parameters and hence reconstructions of the rotation speed using the method of generalized cross validation to select the smoothing parameter. It is shown that this method is analogous to using generalized singular value decomposition to calculate the generalized eigenvalues of the kernel and smoothing matrices. It is demonstrated that this method provides an estimate of the smoothing parameter which leads to a reconstruction of the rotation rate which is close to the best that can be obtained using quadratic regularization. It is also shown that the way in which the integral is discretized is potentially important in ensuring that the estimate of the smoothing function is reliable at all radii.
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