Sadly, the reconstituted model f(A) does not go through, or in some
cases anywhere near, the observed values.
I would have accepted close misses

Hi. Just throwing something out.
It appears that you are trying to work in the frequency domain based on
your Cosine Matrix. It appears to me you want a solution with Cosine's
only. If so, how about the Fourier equation? You can't get an exact
fit without the Sin portion to give you the correct phase shift for each
frequency. Here is the equation. Note that your 18 points are now
numbered 0-17, and not 1-18.

Sub Demo()
Dim Pi As Double
Dim j As Long

For j = 0 To 17
Debug.Print j; CosFit(j)
Next j
End Sub



Function CosFit(x)
Dim Pi As Double
Pi = [Pi()]
CosFit = _
0.886111111111111 + _
0.018898028106003 * Cos(0.724019780381624 - (Pi * x) / 9) + _
0.133429937703512 * Cos(2.32511875642987 - (2 * Pi * x) / 9) + _
6.42910050732863E-02 * Cos(0.679775646576795 + (Pi * x) / 3) + _
0.01522892397659 * Cos(1.81176681414226 - (4 * Pi * x) / 9) + _
6.46080465147374E-02 * Cos(1.59530802116179 + (5 * Pi * x) / 9) + _
1.89866749895945E-02 * Cos(1.99286012557845 + (2 * Pi * x) / 3) + _
7.58641866384528E-03 * Cos(0.708758198743175 + (7 * Pi * x) / 9) + _
3.56086325212297E-03 * Cos(2.77704553008904 - (8 * Pi * x) / 9) + _
2.16666666666666E-02 * Cos(Pi * x)

End Function


Note that your 18 points are divided into 360 (ie 2 Pi/18 - Pi/9)

Here are the results:

0 0.87
1 0.8
2 1
3 1
4 0.98
5 0.98
6 0.98
7 0.75
8 0.65
9 0.69
10 0.97
11 0.98
12 1
13 0.98
14 0.95
15 0.73
16 0.77
17 0.87


Which match what you wanted for the output:

f(A) =
{0.87,0.8,1,1,0.98,0.98,0.98,0.75,0.65,0.69,0.97,0 .98,1,0.98,0.95,0.73,0.77,0.87}



Probably not useful, but I thought I would mention it.

= = =
Dana DeLouis