On Tuesday, 17 May 2016 at 07:47:58 UTC, Ethan Watson wrote:
Unless you're doing game/graphics work ;-) 4x3 or 4x4 matrices
are commonly used to represent transforms in 3D space in every
3D polygon-based rendering pipeline I know of. It's even a
requirement for fixed-function OpenGL 1.x.
Video games - also known around here as "The Exception To The
Rule".
(Side note: My own preference is to represent transforms as a
quaternion and vector. Inverting such a transform is a simple
matter of negating a few components. Generating a matrix from
such a transform for rendering purposes is trivial compared to
matrix inversion.)
I don't know much about computer graphics, but if you're solving
equations, then you can use the techniques mentioned above.
Nevertheless, I'm not really sure what would be the fastest
approach to inverting small matrices. I would definitely try the
LU or Cholesky approaches. It might be that for a small matrix a
Gaussian reduction approach would be fast. There are some
analytic tricks you could use if you have some information about
them, like when you can represent them as blocks. If some of the
blocks are zero or identity matrices, then it simplifies the
calculations too.
