Modified moving least squares with polynomial bases for scattered data approximation

作者：Joldes Grand Roman^*; Chowdhury Habibullah Amin; Wittek Adam; Doyle Barry; Miller Karol

来源：Applied Mathematics and Computation, 2015, 266: 893-902.

DOI：10.1016/j.amc.2015.05.150

• Moving least squares
• Random point distribution
• Scattered data approximation
• Robust shape function generation

One common problem encountered in many fields is the generation of surfaces based on values at irregularly distributed nodes. To tackle such problems, we present a modified, robust moving least squares (MLS) method for scattered data smoothing and approximation. The error functional used in the derivation of the classical MLS approximation is augmented with additional terms based on the coefficients of the polynomial base functions. This allows quadratic base functions to be used with the same size of the support domain as linear base functions, resulting in better approximation capability. The increased robustness of the modified MLS method to irregular nodal distributions makes it suitable for use across many fields. The analysis is supported by several univariate and bivariate examples.

• 出版日期2015-9-1