Ansatz (Ger., "anset, onset, or outset"; plural: Ansätze) is a term often used by physicists and mathematicians. An ansatz is the establishment of the starting equation(s) describing a mathematical or physical problem. It can take into consideration boundary conditions. After an ansatz has been established, the equations are solved for the general function of interest. Typically, a word problem starts by writing down the ansatz with subsequent refinement leading to the solution of the problem. An ansatz is a wise guess that is legitimated later by its results. German (called Deutsch in German; in German the term germanisch is equivalent to English Germanic), is a member of the western group of Germanic languages and is one of the worlds major languages. ... Many famous physicists of the 20th and 21st century are found on the list of recipients of the Nobel Prize in physics. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... This article does not cite any references or sources. ...

For example, 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. In mathematics, a set can be thought of as any collection of distinct objects considered as a whole. ... Look up cluster in Wiktionary, the free dictionary. ... The factual accuracy of this article is disputed. ... In regression analysis, least squares, also known as ordinary least squares analysis, is a method for linear regression that determines the values of unknown quantities in a statistical model by minimizing the sum of the residuals (the difference between the predicted and observed values) squared. ... Calculus of variations is a field of mathematics which deals with functions of functions, as opposed to ordinary calculus which deals with functions of numbers. ... It has been suggested that this article or section be merged with estimation. ...

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 ansatz is to suppose the solutions of a homogeneous linear differential equation and difference equation to have, respectively, exponential and power form. More generally one can guess a particular solution of a system of equations and test such an ansatz by direct substitution of the solution in the system of equations. A simulation of airflow into a duct using the Navier-Stokes equations A differential equation is a mathematical equation for an unknown function of one or several variables which relates the values of the function itself and of its derivatives of various orders. ... In mathematics, a recurrence relation, also known as a difference equation, is an equation which defines a sequence recursively: each term of the sequence is defined as a function of the preceding terms. ...

See also

• Ersatz
• Guesstimate