Estimating the expansion coefficients of a geomagnetic field model using first-order derivatives of associated Legendre functions. (2nd November 2018)

• Record Type: Journal Article
• Authors: Bücker, H. Martin; Willkomm, Johannes
• Is Part Of: Optimization methods and software. Volume 33:Number 4/6(2018)
• Page Start: 924
• Page End: 944
• Publication Date: 2018-11-02
• Subjects: associated Legendre functions -- spherical harmonics -- magnetic field model -- Magsat data -- automatic differentiation -- ADiMat; 33C55 -- 86A25 -- 68N19 -- 65Y99 -- 65F20; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2018.1448086
• Languages: English
• ISSNs: 1055-6788

Abstract

Abstract : The associated Legendre functions are defined on a closed interval. Thus, their derivatives do not exist at the endpoints of the interval. However, one-sided derivatives may exist at the endpoints if the ordinary limit is replaced by a one-sided limit. When computer models that evaluate associated Legendre functions at an endpoint are transformed by automatic differentiation, an approach is needed that is tailored to one-sided derivatives. Rather than employing a black-box approach of automatic differentiation, a hierarchical approach is introduced that is based on analytic first-order one-sided derivatives of the associated Legendre functions at the endpoints. This hierarchical approach is implemented in the automatic differentiation software ADiMat and its feasibility is demonstrated in a parameter estimation problem arising from geomagnetic field modelling.