scholarly journals A Local Radial Basis Function Method for the Laplace–Beltrami Operator

2021 ◽  
Vol 86 (3) ◽  
Author(s):  
Diego Álvarez ◽  
Pedro González-Rodríguez ◽  
Manuel Kindelan
Keyword(s):  
Radial Basis Function ◽  
Basis Function ◽  
Function Method ◽  
Beltrami Operator ◽  
Radial Basis ◽  
Radial Basis Function Method

scholarly journals A symmetric integrated radial basis function method for solving differential equations

2018 ◽  
Vol 34 (3) ◽  
pp. 959-981 ◽  
Author(s):  
Nam Mai-Duy ◽  
Deepak Dalal ◽  
Thi Thuy Van Le ◽  
Duc Ngo-Cong ◽  
Thanh Tran-Cong
Keyword(s):  
Differential Equations ◽  
Radial Basis Function ◽  
Basis Function ◽  
Function Method ◽  
Radial Basis ◽  
Radial Basis Function Method

Accuracy of the Hill–radial basis function method and the Barrett Universal II formula

2020 ◽  
pp. 112067212090295 ◽  
Author(s):  
Gabor Nemeth ◽  
Laszlo Modis
Keyword(s):  
Radial Basis Function ◽  
Intraocular Lens ◽  
Basis Function ◽  
Function Method ◽  
Theoretical Formula ◽  
Refractive Errors ◽  
Radial Basis ◽  
The Mean ◽  
The Hill ◽  
Radial Basis Function Method

Purpose: The aim was to assess the postoperative results of a biometric method using artificial intelligence (Hill–radial basis function 2.0), and data from a modern formula (Barrett Universal II) and the Sanders–Retzlaff–Kraft/Theoretical formula. Methods: Phacoemulsification and biconvex intraocular lens implantation were performed in 186 cataractous eyes. The diopters of intraocular lens were established with the Hill–radial basis function method, based on biometric data obtained using the Aladdin device. The required diopters of the intraocular lens were also calculated by the Barrett Universal II formula and with the Sanders–Retzlaff–Kraft/Theoretical formula. The differences between the manifest postoperative refractive errors and the planned refractive errors were calculated, as well as the percentage of eyes within ±0.5 D of the prediction error. The mean- and the median absolute refractive errors were also determined. Results: The mean age of the patients was 70.13 years (SD = 10.67 years), and the mean axial length was 23.47 mm (range = 20.72–28.78 mm). The percentage of eyes within a prediction error of ±0.5 D was 83.62% using the Hill–radial basis function method, 79.66% with the Barrett Universal II formula, and 74.01% in the case of the Sanders–Retzlaff–Kraft/Theoretical formula. The mean- and the median absolute refractive errors were not statistically different. Conclusion: Clinical success was the highest when using the biometric method, based on pattern recognition. The results obtained using Barrett Universal II came a close second. Both methods performed better compared to a traditionally used formula.

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