Computational issues by interpolating with inverse multiquadrics: a solution

TL;DR

This paper introduces an efficient method for computing matrix-vector products in inverse multiquadric radial basis function interpolation, significantly improving the solution of large dense linear systems.

Contribution

It presents a novel spectral decomposition-based technique to accelerate matrix-vector multiplications in inverse multiquadric interpolation problems.

Findings

The proposed method reduces computational cost in large systems.

Numerical simulations confirm the efficiency of the approach.

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.