x = A \ B... but I know some of x!

[Kyle Altendorf]

My math/Octave question:
How do I solve (or best fit) Ax=B when I know the form or some values of x?

A bit more background:
I have a set of points on a rigid plate whose positions have been
identified with a camera.  The plate was then rotated about some point
(not the origin) and I am trying to identify that point.  I am already
calculating it using 'x = A \ B' (via QR decomposition produces the
same results) where A and B are m by 3 sets of coordinates (with the
third column filled with 1's) and then extracting the estimated angle
of rotation and center of rotation from x.  The problem is that when I
repeat the measurements, I can't get the repeatability I need in
identifying the center of rotation.  I hope that constraining some
parts of x might improve the repeatability.  I do prescribe the
rotation, so theta is more or less known.

I suppose I should also clarify that I can identify the points about
20 times more consistently than the center of rotation is being
calculated and I am using a set of 32 points.  That's why I am under
the impression I should be able to improve the repeatability.

Even if you simply give me a term for what I'm trying to do so that I
can go research it myself, that would be appreciated.

Thanks,
-kyle