7.3. MACK Example

The performance of MACK algorithm are shown in the following with the help of the mathematical function:

Figure 7.26. Test function contour. The left-bottom corner is the region where the absolute values of the function are higher and therefore where the absolute error of an interpolator is higher.

To demonstrate the performance of the MACK algorithm three cases are executed starting from an initial set of three randomly selected points and for a total of 200 new points in the design space:

Case 1

New points are placed in order to maximize the distance between nearest points in x,y plane (Cross-Validation On Variance):

Figure 7.27. Cross-Validation on Variance maximize the distance between nearest points in x,y plane

Case 2

New points are located in order to minimize the relative interpolation error (Cross-Validation On Relative Error):

Figure 7.28. Cross-Validation on Relative Error minimize the relative interpolation error

Case 3

New points are located in order to minimize the absolute interpolation error (Cross-Validation on Absolute Error):

Figure 7.29. Cross-Validation on Absolute Error minimize the absolute interpolation error