Theory and Modern Applications
Table 1 Error measurement for 36 data points
Test function | Method | α | β | γ | Max. Error | COD, \(r^{2}\) |
|---|---|---|---|---|---|---|
\(F_{1}\) | Proposed scheme | 0 | 0 | 0 | 0.039572002 | 0.999132192 |
0.5 | 0.5 | 0.5 | 0.039356921 | 0.999204443 | ||
1 | 1 | 1 | 0.039213533 | 0.999138736 | ||
1.5 | 1.5 | 1.5 | 0.039111114 | 0.999036026 | ||
2 | 2 | 2 | 0.041233549 | 0.998928491 | ||
RBF | Linear | 0.100592819 | 0.990108009 | |||
Thin plate | 0.061040889 | 0.995850492 | ||||
Gaussian | 0.084318638 | 0.99640404 | ||||
Multiquadric | 0.084426575 | 0.99662431 | ||||
\(F_{2}\) | Proposed scheme | 0 | 0 | 0 | 0.005224831 | 0.9996762 |
0.5 | 0.5 | 0.5 | 0.00383375 | 0.999868479 | ||
1 | 1 | 1 | 0.003640571 | 0.999877156 | ||
1.5 | 1.5 | 1.5 | 0.004622681 | 0.999824818 | ||
2 | 2 | 2 | 0.005359263 | 0.999753554 | ||
RBF | Linear | 0.030205436 | 0.9882400797 | |||
Thin plate | 0.0194237841 | 0.9971092186 | ||||
Gaussian | 0.0152887078 | 0.9959802861 | ||||
Multiquadric | 0.0140906173 | 0.9986480384 | ||||
\(F_{3}\) | Proposed scheme | 0 | 0 | 0 | 0.010297668 | 0.999276574 |
0.5 | 0.5 | 0.5 | 0.00987087 | 0.99944839 | ||
1 | 1 | 1 | 0.009586338 | 0.999406891 | ||
1.5 | 1.5 | 1.5 | 0.010848494 | 0.999300821 | ||
2 | 2 | 2 | 0.012001733 | 0.99917947 | ||
RBF | Linear | 0.0424166949 | 0.9849374405 | |||
Thin plate | 0.0150483752 | 0.9973779354 | ||||
Gaussian | 0.0066207785 | 0.9996125352 | ||||
Multiquadric | 0.0118318689 | 0.9983230304 | ||||
\(F_{4}\) | Proposed scheme | 0 | 0 | 0 | 0.011508552 | 0.999061755 |
0.5 | 0.5 | 0.5 | 0.005094778 | 0.999815278 | ||
1 | 1 | 1 | 0.001505409 | 0.999988162 | ||
1.5 | 1.5 | 1.5 | 0.002235251 | 0.999950281 | ||
2 | 2 | 2 | 0.004525884 | 0.999833621 | ||
RBF | Linear | 0.0229660224 | 0.9923793242 | |||
Thin plate | 0.0192271638 | 0.9968560279 | ||||
Gaussian | 0.0568475999 | 0.9728441577 | ||||
Multiquadric | 0.0235599265 | 0.9958461131 | ||||