Numerical Cubature on Scattered Data by Radial Basis Functions

We study cubature formulas on relatively small scattered samples in the unit square, obtained by integrating radial basis function (RBF) interpolants. Numerical tests show that, due to the small size of the corresponding weights (which are not all positive in general), thin-plate splines and Wendland's compactly supported radial functions give the most reliable RBF cubature methods. AMS Subject Classification: 65D05, 65D32. Key words: numerical integration, scattered data, radial basis functions.

• Type: Journal
• Year: 2006
• Where: COMPUTING
• Authors: Alvise Sommariva, Marco Vianello
• Keywords: COMPUTING 2006, Radial Basis Functions, Reliable Rbf Cubature, Small Scattered Samples