Given a
set of experimental data that looks to be
clustered about a line, a linear ansatz could be made to find the
parameters of the line by a
least squares curve fit.
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. ==See also==