Moving least squares approximation using variably scaled discontinuous weight function

Authors : Mohammad Karimnejad Esfahani, Stefano De Marchi, Francesco Marchetti

Pages : 38-54

Doi:10.33205/cma.1247239

View : 18 | Download : 9

Publication Date : 2023-03-15

Article Type : Research

Abstract :Functions with discontinuities appear in many applications such as image reconstruction, signal processing, optimal control problems, interface problems, engineering applications and so on. Accurate approximation and interpolation of these functions are therefore of great importance. In this paper, we design a moving least-squares approach for scattered data approximation that incorporates the discontinuities in the weight functions. The idea is to control the influence of the data sites on the approximant, not only with regards to their distance from the evaluation point, but also with respect to the discontinuity of the underlying function. We also provide an error estimate on a suitable piecewise Sobolev Space. The numerical experiments are in compliance with the convergence rate derived theoretically.
Keywords : MLS approximation, Meshfree methods, Variably scaled discontinuous kernels, Discontinuous function approximation