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

Kazem, Saeed; Chadwick, Edmund A.; Hatam, Ali

Abstract

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. The condition number of the interpolation matrix arising from this basis is of order 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.

Citation

Kazem, S., Chadwick, E. A., & Hatam, A. (2018). Making conditionally negative definite radial basis function interpolation well-conditioned by adding cardinal basis functions. Ain Shams Engineering Journal ASEJ / Ain Shams University, 9(4), 2587-2598. https://doi.org/10.1016/j.asej.2017.03.013

• Journal Article Type: Article
• Online Publication Date: Oct 12, 2017
• Publication Date: Dec 28, 2018
• Deposit Date: Jul 3, 2023
• Publicly Available Date: Jul 3, 2023
• Journal: Ain Shams Engineering Journal
• Print ISSN: 2090-4479
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 9
• Issue: 4
• Pages: 2587-2598
• DOI: https://doi.org/10.1016/j.asej.2017.03.013
• Keywords: General Engineering