Computational issues by interpolating with inverse multiquadrics: a solution

Abstract

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.

De Marchi S., Egidi N., Giacomini J., Maponi P., Perticarini A. (2022) "Computational issues by interpolating with inverse multiquadrics: a solution " Dolomites Research Notes on Approximation, 15(5), 56-64. DOI: 10.14658/PUPJ-DRNA-2022-5-6  
Year of Publication
2022
Journal
Dolomites Research Notes on Approximation
Volume
15
Issue Number
5
Start Page
56
Last Page
64
Date Published
12/2022
ISSN Number
2035-6803
Serial Article Number
6
DOI
10.14658/PUPJ-DRNA-2022-5-6
Issue
Section
SpecialIssue5