🚀 go-pugleaf

Hello!

I have some questions concerning methods for solving large sets 
of mostly nonlinear equations (it's a kind of constraint solving problem).
 
I am seeking for methods to decompose a possible large set of
equations into sets of smaller ones which have to be solved
simultaneously in a certain order. Using a bipartite graph with 
vertices representing the equations and variables 
and undirected arcs representing
the "belongs-to" relationship, one may use a maximum-matching algorithm
to determine a partition into smaller sets. My question is, are there
any other techniques, especially techniques which allow a better 
control of the quality of the generated partition (e.g. number of sets of
more than one equation is minimal)?

Having a set of equations which have to be solved simultaneously, I am
further interested in methods for eliminating as much variables as
possible before solving it using Newton-Raphson iteration. Having for
example a set of 4 equations determining the variables a, b, c, d:

	1. a = f (c, d)
	2. b = g (a, c)
	3. c = h (d)
	4. d = i (b)

the system is reducible to the equation:

	b = g (f (h (i (b)), i (b)), h (i (b)))
or
	d = i (g (f (h (d), d), h (d)))

which may be easier to solve using Newton-Raphson. Knowing wich equation 
has to be solved for which variable, the problem has probably something
to do with finding the feedback vertices in strong components of
directed graphs, a problem known to be NP-complete. Again, my question is
are there any other techniques or heuristics which solve this problem
or special cases perhaps more efficient?

I will thank you for any hints!

+----------------------------+-----------------------------------------+
|                            |                                         |
|  Roland Berling            |  Tel.:   +49 261 9119 436               |
|  Universit"at Koblenz      |  Fax.:   +49 261 9119 499               |
|  Institut f"ur Informatik  |  e-mail: berling@infko.uni-koblenz.de   |
|  Rheinau 3-4               |                                         |
|  D-5400 Koblenz            |                                         |
|  Germany                   |                                         |
|                            |                                         |
+----------------------------+-----------------------------------------+