Inversion of the Limb-Darkening Equation Using the Prony Algorithm
O. R. White · The Astrophysical Journal · 1968
King's interesting application of the Prony algorithm to the inversion of the limb-darkening equation is modified and generalized so that it can be applied rigorously to limb-darkening curves, spectral line profiles, and multiplet line intensities Since King's formulation requires physically inaccessible observa- tions, a change of variable is introduced in the limb-darkening integral to avoid this difficulty Calcula- tions on noisy data confirm the seff -limiting property of this inversion method An approximate method for constructing the smooth S(r) distribution from the slab solution is presente