Recursive moving least squares

The meshless moving least squares (MLS) is expanded here based on recursive least squares (RLS) where the outcome is the newly developed recursive moving least squares (RMLS) approximation method. In RMLS method each nodal point has its own size of the support domain; accordingly, the number of field points on the influence domain varies from node to node. This method makes it possible to select the optimal size of the support domain by imposing any arbitrary measures such as precision or convergence of the unknown parameters on the support domain. Moreover, the possibility of applying the statistical test in removing any undesired outliers of function values is provided. Another feature of this newly developed method is providing the possibility of revealing the significant break-lines and faults diagnosis on the surface. In RMLS the radius of the support domain would become extended to a point where the optimal precision of unknown parameters is achieved or reach the discontinuous or high gradient interfaces. The numerical results indicate that this method improves the accuracy of approximated surface more than 50%, especially for rough surfaces or the contaminated particles by random or gross errors, with no significant increase in time.