Optimizing the coefficients of basis functions to fit a curve
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I have 3 vectors F1, F2, and F3. I want to linearly combine these vectors such that I create a new function W(z)=a*F1+b*F2+c*F3, where a,b,c are just constant coefficients and the 3 vectors are essentially basis functions. These vectors are 1x70 doubles, and are shown plotted below (note that the horizontal axis 'Range' is the 'z'-variable in the equations below).
The problem I am having is finding a way to calculate the coefficients a,b,c so that W=a*F1+b*F2+c*F3 most closely matches a function given by:
Plotted together, W and r are shown below...
What sort of optimization process can I use to build a function W=a*F1+b*F2+c*F3 that fits 'W' to 'r' and returns the coefficients a,b,c used to do so? Please note that F1,F2, and F3 are all 1x70 doubles, and are not explicitly functions of z anymore. They have each individually been evaluated. And so I tried using the curvefitting app with no success because of this. I really just need a systematic way to optimize the coefficients a,b, and c. Is there a built in way to do this?