Theory and Modern Applications
Table 2 Error measurement for 65 data points
Test function | Method | α | β | γ | Max. Error | COD, \(r^{2}\) |
|---|---|---|---|---|---|---|
\(F_{1}\) | Proposed scheme | 0 | 0 | 0 | 0.02687835 | 0.99970822 |
0.5 | 0.5 | 0.5 | 0.024962602 | 0.999784795 | ||
1 | 1 | 1 | 0.023685436 | 0.999784545 | ||
1.5 | 1.5 | 1.5 | 0.022773175 | 0.99975924 | ||
2 | 2 | 2 | 0.022088979 | 0.999726521 | ||
RBF | Linear | 0.066757877 | 0.996406813 | |||
Thin plate | 0.045039467 | 0.998917027 | ||||
Gaussian | 0.051615474 | 0.998943393 | ||||
Multiquadric | 0.045394416 | 0.999293455 | ||||
\(F_{2}\) | Proposed scheme | 0 | 0 | 0 | 0.00495738 | 0.9997997 |
0.5 | 0.5 | 0.5 | 0.002339451 | 0.999959285 | ||
1 | 1 | 1 | 0.00132277 | 0.999983602 | ||
1.5 | 1.5 | 1.5 | 0.00249288 | 0.999960772 | ||
2 | 2 | 2 | 0.003486274 | 0.999921666 | ||
RBF | Linear | 0.024103813 | 0.996780746 | |||
Thin plate | 0.008553969 | 0.999517773 | ||||
Gaussian | 0.00777573 | 0.999676093 | ||||
Multiquadric | 0.003075157 | 0.999930748 | ||||
\(F_{3}\) | Proposed scheme | 0 | 0 | 0 | 0.005796483 | 0.999751766 |
0.5 | 0.5 | 0.5 | 0.005918016 | 0.999871966 | ||
1 | 1 | 1 | 0.006761969 | 0.999854954 | ||
1.5 | 1.5 | 1.5 | 0.007657692 | 0.999795222 | ||
2 | 2 | 2 | 0.008385618 | 0.999724403 | ||
RBF | Linear | 0.042058919 | 0.992260381 | |||
Thin plate | 0.017086633 | 0.999009874 | ||||
Gaussian | 0.003776303 | 0.999890903 | ||||
Multiquadric | 0.005425971 | 0.999869049 | ||||
\(F_{4}\) | Proposed scheme | 0 | 0 | 0 | 0.007096203 | 0.999570807 |
0.5 | 0.5 | 0.5 | 0.003041664 | 0.999923419 | ||
1 | 1 | 1 | 0.001107079 | 0.999995758 | ||
1.5 | 1.5 | 1.5 | 0.001847266 | 0.99996772 | ||
2 | 2 | 2 | 0.003107032 | 0.999903101 | ||
RBF | Linear | 0.018024405 | 0.997033693 | |||
Thin plate | 0.016229475 | 0.998856534 | ||||
Gaussian | 0.044481378 | 0.992096123 | ||||
Multiquadric | 0.018317684 | 0.998719319 | ||||