This must seem like a really elementary question, so please bear with me. Suppose I have a nonlinear system of equations:
where Question. How do I construct a linearization about some point
and there are no intermediate variables Motivation. I have a huge model My progress so far. My attack is as follows:
Unfortunately, Edit: corrected a mistake in the above equation. asked 30 Aug '10, 17:53 Gilead ♦ 
J5 is not square? Don't J1, J2 and J3 have m rows and J4, J5 and J6 have n rows? Anyway, let M = [J2', J5']', which I think is (m+n) by n. Is it rank n? answered 30 Aug '10, 19:00 Paul Rubin ♦♦ Of course! I knew the columnwise partitioning was mnp, but I couldn't figure what the rowwise partitioning was (in retrospect, it was staring me in the face! mn gives a square matrix J5, and all the other inversions will work out). My bad. Thanks for pointing that out. I should mention that J5 can sometimes be rankdeficient  but that's easily handled using a pseudoinverse. Thanks again!
(30 Aug '10, 19:29)
Gilead ♦
