Statements (21)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
mathematical operator
|
| gptkbp:actsOn |
continuous functions on [0,1]
|
| gptkbp:basisFor |
gptkb:Bernstein_polynomials
|
| gptkbp:field |
gptkb:mathematics
approximation theory |
| https://www.w3.org/2000/01/rdf-schema#label |
Bernstein operator
|
| gptkbp:introducedIn |
1912
|
| gptkbp:mapType |
polynomials
|
| gptkbp:namedAfter |
gptkb:Sergei_Natanovich_Bernstein
|
| gptkbp:notation |
Bn(f)(x)
|
| gptkbp:property |
preserves linear functions
preserves positivity converges uniformly to f as n→∞ for continuous f |
| gptkbp:relatedTo |
gptkb:Weierstrass_approximation_theorem
gptkb:Bernstein_polynomial |
| gptkbp:satisfies |
gptkb:Weierstrass_approximation_theorem
|
| gptkbp:type |
linear operator
positive operator |
| gptkbp:usedFor |
approximating continuous functions
|
| gptkbp:bfsParent |
gptkb:Szász–Mirakyan_operator
|
| gptkbp:bfsLayer |
7
|