Editing Ansatz (section)

==Examples==
Given a [[set (mathematics)|set]] of experimental data that looks to be [[Cluster analysis|clustered]] about a line, a linear ansatz could be made to find the [[parameter]]s of the line by a [[least squares]] curve fit. [[Calculus of variations|Variational]] [[approximation]] methods use ansätze and then fit the parameters.

Another example could be the mass, energy, and entropy balance equations that, considered simultaneous for purposes of the elementary operations of [[linear algebra]], are the ansatz to most basic problems of [[thermodynamics]].

Another example of an ansatz is to suppose the solution of a homogeneous linear [[differential equation]] to take an exponential form, or a power form in the case of a [[difference equation]]. More generally, one can guess a particular solution of a system of equations, and test such an ansatz by directly substituting the solution into the system of equations. In many cases, the assumed form of the solution is general enough that it can represent arbitrary functions, in such a way that the set of solutions found this way is a full set of all the solutions.