Accession Number : AD0673383

Title :   ESTIMATING THE RELIABILITY OF LIMB DARKENING FUNCTIONS AND SOURCE FUNCTIONS OBTAINED BY LINEAR LEAST SQUARES FITTING,

Corporate Author : SACRAMENTO PEAK OBSERVATORY SUNSPOT N MEX

Personal Author(s) : White,O. R.

Report Date : 25 JUN 1968

Pagination or Media Count : 39

Abstract : One of the most commonly-used methods for inverting the emergent intensity integral, I(mu) = the integral from 0 to infinity of the quantity (S(tau) exp(-tau/mu)(d tau)/mu), is to fit the data I(mu sub i) with a function for which the Laplace transform is known. Polynomials in mu and ln mu are most convenient because they require only linear least squares fitting of the data. However, such polynomials often lead to physically inadmissable values of S(tau) for the limiting values of tau approaching 0 and tau approaching infinity. So, the question of the range and degree of reliability for such a source function is of interest. Such questions lead directly to error propagation in least squares processes and also to the concept of the weight or error band of a fitted curve. This note discusses the inverse matrix in least squares problems where one variable is known precisely. (Author)

Descriptors :   (*SOLAR ATMOSPHERE, BRIGHTNESS), (*CURVE FITTING, LEAST SQUARES METHOD), STATISTICAL ANALYSIS, MATRICES(MATHEMATICS), UNCERTAINTY, INTEGRAL EQUATIONS, POLYNOMIALS

Subject Categories : Astrophysics
      Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE