What happens when the argument l=1 in spap2 command?

Is only one polynomial fit on the data points. In that case what are the equations solved to obtain the 4 unknowns?

Answer 1

[Joost]

I guess what you mean is the fit of one cubic polynomial (4 unknowns) on an arbitrary large data set of (x, y) pairs. In that case, your equations have been written down nicely at this page.

[Varsha]

But aren't there more constraints in case of spap2 algorithm other than a least square approximation by a cubic polynomial. If that was not the case,spap2 with l=1 and k=4 as well as polyfit of degree 3 would give same fit.But that is not the case.

[Joost]

This might be the weighting factor w (5th argument in spap2 function call). Could you please try with weights set to 1 and check if the result is the same as polyfit? (I do not have the toolbox with spap2 myself). The weights may cause the different result.