Making conditionally negative definite radial basis function interpolation well-conditioned by adding cardinal basis functions

• Main Authors: Saeed Kazem, Edmund A. Chadwick, Ali Hatam
• Format: Article
• Language: English
• Published: Elsevier 2018-12-01
• Series: Ain Shams Engineering Journal
• Online Access: http://www.sciencedirect.com/science/article/pii/S2090447917300916
• ISSN: 2090-4479

A class of basis functions so called well-conditioned RBF (WRBFs) has been introduced. This basis has been manipulated by adding cardinal functions to the conditionally negative definite RBFs of order 1, such as Multiquadric functions 1+(∊r)2 (MQ) and log(1+(∊r)2) (LOG). The condition number of the interpolation matrix arising from this basis is of O(N), where N is the number of center nodes. This order is independent of shape parameter and therefore applying this basis functions would recover the ill–posed linear system associated with the order 1 conditionally negative definite RBFs interpolation. Keywords: Radial basis functions, Cardinal functions, Multiquadrics (MQ), AMS subject classifications: 65M20, 65M06