In mathematics, approximation theory is concerned with how functions can best be approximated with simpler functions, and with quantitatively characterizing...

An approximation is anything that is intentionally similar but not exactly equal to something else. The word approximation is derived from Latin approximatus...

useful approximation for a few terms, but at some point becomes less accurate if even more terms are added. The breakthrough from chaos theory was an...

algorithms achieved the best possible approximation ratio. Hardness of approximation theory deals with studying the approximation threshold of such problems. For...

In number theory, the study of Diophantine approximation deals with the approximation of real numbers by rational numbers. It is named after Diophantus...

Bragg–Williams approximation, models on Bethe lattice, Landau theory, Curie-Weiss law for magnetic susceptibility, Flory–Huggins solution theory, and Scheutjens–Fleer...

needed] two major classes of function approximation problems: First, for known target functions approximation theory is the branch of numerical analysis...

In the mathematical theory of artificial neural networks, universal approximation theorems are theorems of the following form: Given a family of neural...

statistics, however. Non-asymptotic bounds are provided by methods of approximation theory. Examples of applications are the following. In applied mathematics...

calculations in quantum chemistry until the 1990s, when the approximations used in the theory were greatly refined to better model the exchange and correlation...

Automata theory is the study of abstract machines and automata, as well as the computational problems that can be solved using them. It is a theory in theoretical...

In approximation theory, Bernstein's theorem is a converse to Jackson's theorem. The first results of this type were proved by Sergei Bernstein in 1912...

differential equations, differential geometry, probability theory, and approximation theory. Bernstein was born into the Jewish family of prominent Ukrainian...

Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations...

mathematics, Stirling's approximation (or Stirling's formula) is an asymptotic approximation for factorials. It is a good approximation, leading to accurate...

In quantum mechanics, perturbation theory is a set of approximation schemes directly related to mathematical perturbation for describing a complicated...

In computer science and operations research, approximation algorithms are efficient algorithms that find approximate solutions to optimization problems...

analysis using functional analysis and approximation theory; numerical analysis broadly includes the study of approximation and discretization with special focus...

In physics, a gauge theory is a type of field theory in which the Lagrangian, and hence the dynamics of the system itself, does not change under local...

Mathematics: Approximation theory — Arakelov theory — Asymptotic theory — Bifurcation theory — Catastrophe theory — Category theory — Chaos theory — Choquet...

disk. It was proven by Sergei Bernstein while he was working on approximation theory. Let max | z | = 1 | f ( z ) | {\displaystyle \max _{|z|=1}|f(z)|}...

discrete mathematics, graph theory, number theory, mathematical analysis, approximation theory, set theory, and probability theory. Much of his work centered...

Journal of Approximation Theory is "devoted to advances in pure and applied approximation theory and related areas." "Journal of Approximation Theory - Elsevier"...

Coding theory is the study of the properties of codes and their respective fitness for specific applications. Codes are used for data compression, cryptography...

mathematical theories. Almgren–Pitts min-max theory Approximation theory Arakelov theory Asymptotic theory Automata theory Bass–Serre theory Bifurcation theory Braid...

In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called...

In number theory, Dirichlet's theorem on Diophantine approximation, also called Dirichlet's approximation theorem, states that for any real numbers α...

In graph theory, an independent set, stable set, coclique or anticlique is a set of vertices in a graph, no two of which are adjacent. That is, it is a...

Decision theory or the theory of rational choice is a branch of probability, economics, and analytic philosophy that uses expected utility and probability...

Diophantine approximation and transcendental number theory, though for sharp results ad hoc methods—in some sense inspired by the Padé theory—typically...