ABSTRACT
The shape parameter is a significant factor in determining the effectiveness of the interpolation of the Inverse Multi-quadratic Radial Basis Function (IMQ-RBF). This paper utilizes a simulated annealing algorithm to get the best form parameter for various interpolation challenges. The algorithm is evaluated based on interpolation precision, running time, and iteration count. Numerical experimental results show that, compared with other commonly used methods, the algorithm significantly improves interpolation accuracy while ensuring fast parameter selection.
- Franke, R. 1982. Scatteraed data interpolation: tests of some methods. Math. Comput., 38(157), 181-200. https://doi.org/10.1090/S0025-5718-1982-0637296-4.Google ScholarCross Ref
- Kong, Q., Lu, Y., Jiang, G., Liu, Y. 2023. Acoustic measurement of velocity field using improved radial basis function neural network. International Journal of Heat and Mass Transfer, 202, 123733. https://doi.org/10.1016/j.ijheatmasstransfer.2022.123733.Google ScholarCross Ref
- Segeth, K. 2023. Spherical radial basis function approximation of some physical quantities measured. COMPUT APPL MATH, 427, 115128. https://doi.org/10.1016/j.cam.2023.115128.Google ScholarDigital Library
- Rathan, S., & Shah, D. 2022. Construction and Comparative Study of Second Order Time Stepping Methods Based on IQ and IMQ-RBFs. J. Comput. Appl. Math., 8(4), 203. https://doi.org/10.1007/s40819-022-01423-0.Google ScholarCross Ref
- Stein, E. M., & Weiss, G. 1971. Introduction to Fourier analysis on Euclidean spaces (Vol. 1). Princeton university press. https://www.jstor.org/stable/j.ctt1bpm9w6.Google Scholar
- Ghalichi, S. S. S., Amirfakhrian, M., & Allahviranloo, T. 2022. An algorithm for choosing a good shape parameter for radial basis functions method with a case study in image processing. Results in Applied Mathematics, 16, 100337. https://doi.org/10.1016/j.rinam.2022.100337.Google ScholarCross Ref
- Liu, C. Y., & Ku, C. Y. 2022. A simplified radial basis function method with exterior fictitious sources for elliptic boundary value problems. MATHEMATICS-BASEL, 10(10), 1622. https://doi.org/10.3390/math10101622.Google ScholarCross Ref
- Zhou, X., Dong, C., Zhao, C., & Bai, X. 2020. Temperature-field reconstruction algorithm based on reflected sigmoidal radial basis function and QR decomposition. Appl. Therm. Eng., 171, 114987. https://doi.org/10.1016/j.applthermaleng.2020.114987.Google ScholarCross Ref
- Papaioannou, P. G., Talmon, R., Kevrekidis, I. G., & Siettos, C. 2022. Time-series forecasting using manifold learning, radial basis function interpolation, and geometric harmonics. CHAOS, 32(8), 083113. https://doi.org/10.1063/5.0094887.Google ScholarCross Ref
- Xiang, S., Wang, K. M., Ai, Y. T., Sha, Y. D., Shi, H. 2012. Trigonometric variable shape parameter and exponent strategy for generalized multiquadric radial basis function approximation. APPL MATH MODEL 36(5), 1931-1938. https://doi.org/10.1016/j.apm.2011.07.076.Google ScholarCross Ref
- Da Silva, E. R., Manzanares-Filho, N. 2010. Metamodeling for global optimization using radial basis functions with cross-validation adjustment of the shape parameter. In 2nd International Conference on Engineering Optimization, EngOpt. http://www.dem.ist.utl.pt/engopt2010/Book_and_CD/Papers_CD_Final_Version/pdf/09/01321-01.pdf.Google Scholar
- Mojarrad, F. N., Veiga, M. H., Hesthaven, J. S, Öffner, P. 2023. A new variable shape parameter strategy for RBF approximation using neural networks. Comput. Math. Appl., 143, 151-168.https://doi.org/10.1016/j.camwa.2023.05.005Google ScholarDigital Library
- Rippa, S. 1999. An algorithm for selecting a good value for the parameter c in radial basis function interpolation. Adv. Comput. Math., 11, 193-210. https://doi.org/10.1023/A:1018975909870.Google ScholarCross Ref
- Sivaram, S. A., & Vinoy, K. J. 2020. Inverse multiquadric radial basis functions in eigenvalue analysis of a circular waveguide using radial point interpolation method. IEEE Microwave Wireless Compon. Lett., 30(6), 537-540. https://doi.org/10.1109/LMWC.2020.2992372.Google ScholarCross Ref
- Cheng, A. D. 2012. Multiquadric and its shape parameter—a numerical investigation of error estimate, condition number, and round-off error by arbitrary precision computation. Eng. Anal. Boundary Elem., 36(2), 220-239. https://doi.org/10.1016/j.enganabound.2011.07.008.Google ScholarCross Ref
- Kaveh, A., & Jafari Vafa, J. 2022. Simulated annealing algorithm for selecting the suboptimal cycle basis of a graph. Int J Optim Civ Eng, 12(2), 234-243. http://ijoce.iust.ac.ir/article-1-518-en.pdf.Google Scholar
Index Terms
- Selection Method of Shape Parameters in IMQ-RBF Interpolation Based on Simulated Annealing Algorithm
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