Constructing atom-molecule potential surfaces from ab initio data: A method combining quadrature and interpolation (Q1581135)

This paper is concerned with the approximation of a smooth function \(F(\theta ,\phi)\) (the potential surface) defined in the unit sphere, given the value of the function at a limited number of points \((\theta _i, \phi _l)\). In order to minimize the number of sampling points required to generate a reliable potential surface, the author proposes a two-step process. The first step uses a quadrature-based approximation to \(F\) which is improved in the second step by a correction term interpolating the residual difference between the approximation and the unknown function at the quadrature nodes. Numerical experiments show the higher global accuracy than does a method based on quadrature only.