Does anyone know what interpolation method is used by default for the following operation?
i) rotation
ii) zoom

I've tried to look for this info on the Internet, but so far I have no idea of the answer...

Inkscape is not a raster program, so if i understand your question correctly, there is no interpolation going on for rotation and zooming, because the vector objects are described as connected points. of course you might be specifically asking about what method is used for imported or converted bitmaps and if that is the case, the only info i can give you is that there is a setting for bitmap oversampling in the preferences, the default setting is 2x2.

What exactly do you mean when you say that "vector objects are described as connected points"?
Let us suppose that I have a generic RGB picture (a painting, for instance). I open it with Inkscape and I do a 3x zoom of a small square inside that. An interpolation method has to used to get the final result, isn't it?

Correct. That would be an example of

imported or converted bitmaps

I don't quite understand your example though. A 3X zoom would just show you the same pixels, only bigger. There is no raster program either that will 'interpolate' for a positive zoom. Are you talking perhaps about scaling?
Allow me to ask this, and maybe I can offer a better answer: what are you trying to do, and why are you choosing to do it in Inkscape and not in the GIMP?

import a black/white checkerboard, zoom on it. If it's blocky then it's "nearest neighbour", if it's blurry then it's linear (or cubic or...)

Ok, I'll try to be more precise. I want to test the Euclidean Invariance of a filter that I have designed.

To do so, I want to compute the numerical difference between
a) a transformation F (that could be for instance a zoom or a rotation) and then the filter
b) the filter and then the transformation F

However, I need to know the interpolation method used in the design of F, which is a rotation or a zoom. Hence, my question about the interpolation method used by Inkscape. Also GIMP would be fine for me, but I could not find the interpolation method used by default also by GIMP.

What I need to know is if the interpolation method is linear, cubic, sinc(.) and so on...

> compute the numerical difference

Because of quality settings (quality vs time) available to end users, answer will probably be "it depends of user settings"

I think you'd better post this in the dev mailing list, you'll get more accurate response.

http://inkscape.org/mailing_lists.php

> I want to compute the numerical difference between a and b

What will be the practical use if it depends of useragent and/or settings ?

Yes, I agree that "it depends on user settings", but my question still holds, i.e. what is the default? If I just rotate or zoom, what interpolation method is adopted? Analogously, where can I find those "user settings"?

The practical use lies in the fact that I want to write the interpolation method adopted, so that the whole experiment is reproducible.

For such a technical question, dev list will provide better answers.

This doesn't answer your question but, I suppose inkscape qualifies for Hiquality SVG viewer, so, if your svg contains an "image-rendering" directive set as "optimizeQuality" then it should render (at least) using bilinear resampling.

http://www.w3.org/TR/SVG/painting.html# ... ngProperty