Thank you Francois.
Actually his review appears to have been focussing on another product from the same company called FocusFixer, but he seems to be using SizeFixer too.
I have sent him a short email to check the status.
These products are fascinating in what they claim to achieve.
Just a wild guess, but they could be using an optimization technique called "simulated annealing" ("recuit simule" en Francais) that has been promising for many years but extremelly demanding in terms of computational power.
Basically it is based on the definition of a metrics (in this case the sharpness of the image I assume) and by an iterative process that attempts to minimize this metrics by trying out different random solution around a first good guess. In the case of enlargement, the best enlargement is probably the one that is closest to the original image when interpolated back down. The particularity of the technique is that it is good at avoiding wrong local minima that other optimization techniques often converge to.
http://en.wikipedia.org/wiki/Simulated_annealingThanks again.
Regards,
Bernard