On Tuesday, August 9, 2022 at 1:38:07 PM UTC-4 Florian Königstein wrote:

> Some time ago I tried whether analytical calculation of the partial 
> derivatives is better (faster convergence). I wrote code for analytical 
> calculation (via automatic differentiation), but it seemed that there was 
> no advantage (longer time and little or no reduction in the number of 
> iterations).
>

I had somehow missed the fact that the term "automatic differentiation" 
meants that and I thought "analytical" meant symbolic.  Now that I googled 
it again, I see what I'm talking about is within the scope of "automatic 
differentiation".  Of course, the devil is in the details.  If you do it 
right, I would not expect it to be slower per iteration than finite 
difference in the pano13 problem space (but I won't know until I try, as it 
can take twice as long in some problem spaces).  As you found, I also would 
not expect a typical reduction in number of iterations.  More accurate 
derivatives typically provides little benefit in the common cases.  Its 
benefit should be in reducing the number of pathological cases.
But I'm more interested now in the possible speedup (per iteration) 
relative to finite difference (most, but not all, of which comes from 
assuming an average of more than one image per lens).

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