Numerical Algebraic Approach
Numerical constraint solvers function by first translating the
constraints into a system of algebraic equations. This system is then
solved using an iterative technique such as the Newton-Raphson method.
Clearly, numerical methods are an example of
A positive feature of this approach is that it is able to handle
but consistent problems which other techniques may not
be able to solve, assuming convergence.
For this reason, many constraint solvers fall back
on iterative techniques when the native method is not sufficient to
solve a given configuration.
However, there are some serious drawbacks with the numerical approach.
First is the problem that of the potentially exponential number of
solutions, iterative methods can produce only a single solution.
Also, the solution to which it converges depends strongly on the initial
configuration. Furthermore, because of the multiple solutions and the
large number of parameters, the constraint solving problem is often
ill-conditioned, making convergence difficult or impossible.
- L. A. Barford 
- A. H. Borning 
- J. Gosling 
- G. Nelson 
- R. Light and D. Gossard 
- I. Sutherland 
- A. Witkin, K. Fleischer, and A. Barr