https://scholars.lib.ntu.edu.tw/handle/123456789/630504
標題: | Residual-Error Cross-Validation method for selecting a suitable shape parameter for RBF interpolation | 作者: | Kuo, L. H. Uvah, Jossy CHUIN-SHAN CHEN |
關鍵字: | LOOCV | Optimization | Radial basis functions | Residual errors | Shape parameter | 公開日期: | 1-十月-2022 | 出版社: | ELSEVIER SCI LTD | 卷: | 143 | 起(迄)頁: | 331 | 來源出版物: | Engineering Analysis with Boundary Elements | 摘要: | Radial 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. |
URI: | https://scholars.lib.ntu.edu.tw/handle/123456789/630504 | ISSN: | 09557997 | DOI: | 10.1016/j.enganabound.2022.06.021 |
顯示於: | 土木工程學系 |
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