Kuo, L. H.L. H.KuoUvah, JossyJossyUvahCHUIN-SHAN CHEN2023-04-242023-04-242022-10-0109557997https://scholars.lib.ntu.edu.tw/handle/123456789/630504Radial Basis Functions (RBFs) have shown the potential to be a universal mesh-free method for solving interpolation and differential equations with highly accurate results. However, the trade-off principle states that while deciding the shape parameter's value for an RBF such as Multiquadric (MQ) or Gaussian (GA), a compromise must be made between achieving accuracy and stability because of the resultant ill-conditioned matrix. This study focus on the behaviors between the maximum and residual errors for the RBF interpolation. Based on the error behaviors, we propose a new approach, Residual-Error Cross Validation (RECV), to quickly select a suitable c value for an interpolant using an RBF containing a shape parameter. The numerical results showed that an RBF interpolant could yield high accuracy with the RECV c and a sufficiently small fill distance. Combining the RECV method and LOOCV method, we can easily avoid the local optimum issue when applying an optimization algorithm.LOOCV | Optimization | Radial basis functions | Residual errors | Shape parameterjournal article10.1016/j.enganabound.2022.06.0212-s2.0-85133878351WOS:000828303900002https://api.elsevier.com/content/abstract/scopus_id/85133878351