Fast radial basis function interpolation with Gaussians by localization and iteration

Global field interpolation for particle methods

“…The disadvantage is that one must still build and solve a large linear system. However, in another concurrent work, a fast algorithm to solve this system in OðNÞ operations has been developed and demonstrated in practice [35].…”

Comparing seven spectral methods for interpolation and for solving the Poisson equation in a disk: Zernike polynomials, Logan–Shepp ridge polynomials, Chebyshev–Fourier Series, cylindrical Robert functions, Bessel–Fourier expansions, square-to-disk conformal mapping and radial basis functions

“…In spite of its great cost, this option is widely used with radial basis functions (RBF) because of its simplicity. A much faster procedure is to use a so-called Fast Summation to sum RBF series and a preconditioned iteration, repeatedly calling a Fast Summation routine, for interpolation [98,26]. Because these routines are complicated, they are not yet widely used with RBFs, so Table 7 lists the costs for both direct and iterative RBF interpolation.…”

A level set method for topological shape optimization of 3D structures with extrusion constraints

“…In fact, despite the attractive features of the RBF interpolation, this method will always generate a linear system with a dense, ill-conditioned matrix, with the computational complexity of O(N ), =2,3 [38].…”