RANDOM  INTERPOLATION

Quality Factors (Reproduced value &
Cross-Validation, 4D)

The sample function has the analytic form:

f(x1, x2, x3, x4 ) = x12 + x22 + 2 x32 + x42- 5 x1 - 5 x2 - 21 x3 + 7 x4 + 50.

(This is the so-called Rosen-Suzuki function.)

where   -10. < x1 < +10. and   -10. < x2 < +10.
            -10. < x3 < +10. and   -10. < x4 < +10.

For this comparison case, we have used 72 random locations together with the associated function values to construct the interpolant. Also, delta width values of X1, X2, X3 and X4 are the same and are chosen to be 2 and 2.5 for comparison.

INPUT AREA

Input Location Number (M'):

Location NumberInput x1Input x2Input x3Input x4Input Function
f(x1, x2, x3, x4)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72

Two quality factors, "reproduced function value" and "cross-validation function value" are tabulated below for the first 15 input locations. The first table is for delta width equal to 2 and the second table is for the delta width equal to 2.5.

TABLE 1

TABLE 2

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