Ansatz
In
Use
An ansatz is the establishment of the starting equation(s), the theorem(s), or the value(s) describing a mathematical or physical problem or solution. It typically provides an initial estimate or framework to the solution of a mathematical problem,[3] and can also take into consideration the boundary conditions (in fact, an ansatz is sometimes thought of as a "trial answer" and an important technique in solving differential equations[2]).
After an ansatz, which constitutes nothing more than an assumption, has been established, the equations are solved more precisely for the general function of interest, which then constitutes a confirmation of the assumption. In essence, an ansatz makes assumptions about the form of the solution to a problem so as to make the solution easier to find.[4]
It has been demonstrated that machine learning techniques can be applied to provide initial estimates similar to those invented by humans and to discover new ones in case no ansatz is available.[5]
Examples
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
See also
![](http://upload.wikimedia.org/wikipedia/commons/thumb/9/99/Wiktionary-logo-en-v2.svg/40px-Wiktionary-logo-en-v2.svg.png)
- Method of undetermined coefficients
- Bayesian inference
- Bethe ansatz
- Coupled cluster, a technique for solving the many-body problem that is based on an exponential Ansatz
- Demarcation problem
- Guesstimate
- Heuristic
- Hypothesis
- Trial and error
- Train of thought
References
- ^ "Definition of ANSATZ". www.merriam-webster.com. Retrieved 2019-11-19.
- ^ OCLC 39147817.
- ^ "Definition of ANSATZ". www.merriam-webster.com. Retrieved 2019-11-19.
- ^ "Ansatz | Definition of Ansatz by Lexico". Lexico Dictionaries | English. Archived from the original on October 26, 2020. Retrieved 2020-10-22.
- .
Bibliography
- Weis, Erich; Heinrich Mattutat (1968), The New Schöffler-Weis Compact German and English Dictionary, Ernst Klett Verlag, Stuttgart, ISBN 0-245-59813-8
- Karbach, M.; Müller, G. (September 10, 1998), Introduction to the Bethe ansatz I. Computers in Physics 11 (1997), 36-43. (PDF), archived from the original (PDF) on September 1, 2006, retrieved 2008-10-25
- Karbach, M.; Hu, K.; Müller, G. (September 10, 1998), Introduction to the Bethe ansatz II. Computers in Physics 12 (1998), 565-573. (PDF), archived from the original (PDF) on September 1, 2006, retrieved 2008-10-25
- Karbach, M.; Hu, K.; Müller, G. (August 1, 2000), Introduction to the Bethe ansatz III. (PDF), archived from the original (PDF) on September 1, 2006, retrieved 2008-10-25