A numerical optimization approach to generate smoothing spherical splines

Here, we are particularly interested in finding smoothing cubic splines that best fit given data in the Euclidean sphere. To achieve this aim, a least squares optimization problem based on the minimization of a certain cost functional is formulated. To solve the problem a numerical algorithm is implemented using several routines from MATLAB toolboxes. The proposed algorithm is shown to be easy to implement, very accurate and precise for spherical data chosen randomly.