Computational issues by interpolating with inverse multiquadrics: a solution

TitleComputational issues by interpolating with inverse multiquadrics: a solution
Publication TypeJournal Article
Year of Publication2022
AuthorsDe Marchi, S, Egidi, N, Giacomini, J, Maponi, P, Perticarini, A
JournalDolomites Research Notes on Approximation
Date Published12/2022
PublisherPadova University Press
Place PublishedPadova, IT
ISSN Number2035-6803

We consider the interpolation problem with the inverse multiquadric radial basis function. The problem usually produces a large dense linear system that has to be solved by iterative methods. The efficiency of such methods is strictly related to the computational cost of the multiplication between the coefficient matrix and the vectors computed by the solver at each iteration. We propose an efficient technique for the calculation of the product of the coefficient matrix and a generic vector. This computation is mainly based on the well-known spectral decomposition in spherical coordinates of the Green’s function of the Laplacian operator. We also show the efficiency of the proposed method through numerical simulations.