specifically functional analysis, a Banach space is said to have the approximation property (AP), if every compact operator is a limit of finite-rank operators...

In the field of machine learning, the universal approximation theorems state that neural networks with a certain structure can, in principle, approximate...

{\displaystyle X} satisfies the bounded approximation property. The first example by Enflo of a space failing the approximation property was at the same time the first...

study the quality of approximation of the Galerkin solution u n {\displaystyle u_{n}} . The analysis will mostly rest on two properties of the bilinear form...

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

In algebra, a commutative Noetherian ring A is said to have the approximation property with respect to an ideal I if each finite system of polynomial equations...

topology. Whether this was true in general for Banach spaces (the approximation property) was an unsolved question for many years; in 1973 Per Enflo gave...

rank and uniformly bounded, such a space V satisfies the bounded approximation property. A Banach space with a Schauder basis is necessarily separable,...

expansion used in the approximation. The expressions: a zeroth-order approximation, a first-order approximation, a second-order approximation, and so forth are...

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

mechanics. The approximation is widely used in quantum chemistry to speed up the computation of molecular wavefunctions and other properties for large molecules...

had been open for more than forty years: The basis problem and the approximation problem and later the invariant subspace problem for Banach spaces....

Approximations for the mathematical constant pi (π) in the history of mathematics reached an accuracy within 0.04% of the true value before the beginning...

related fields, relaxation is a modeling strategy. A relaxation is an approximation of a difficult problem by a nearby problem that is easier to solve....

Chevalley groups, showing that the strong approximation property is restrictive. Superstrong approximation Eichler, Martin (1938), "Allgemeine...

In general, a function approximation problem asks us to select a function among a well-defined class[citation needed][clarification needed] that closely...

goal is to recover properties of such a function f {\textstyle f} without evaluating it directly. Instead, stochastic approximation algorithms use random...

randomness, cryptography, probabilistically checkable proofs, approximation, property testing, spectral graph theory, and sublinear algorithms. He also...

{m}}^{c}} . Ring with the approximation property Popescu's theorem Artin's criterion Artin, Michael (1969), "Algebraic approximation of structures over complete...

several areas of computational complexity, including hardness of approximation, property testing, and interactive proof systems. Lateral computing, alternative...

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

In mathematical analysis, the Weierstrass approximation theorem states that every continuous function defined on a closed interval [a, b] can be uniformly...

In mathematics, a linear approximation is an approximation of a general function using a linear function (more precisely, an affine function). They are...

known for his work on computational learning theory, hardness of approximation, property testing, quantum computation and quantum information. O'Donnell...

174650, S2CID 9706753. Berman, Piotr; Fujito, Toshihiro (1995), "On approximation properties of the Independent set problem for degree 3 graphs", Algorithms...

category Accessible category Algebraic geometry Algebraic stack Approximation property – Mathematical concept Barsotti–Tate group Chern class Crystal (mathematics)...

the total derivative of a function f at a point is the best linear approximation near this point of the function with respect to its arguments. Unlike...

the Hilbert space. This is an immediate consequence of the best approximation property: if y is the element of a closed convex set F closest to x, then...

continuous at the origin. On a reflexive Banach space with the approximation property the following two conditions are equivalent: every quadratic form...

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