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...ttps://books.google.com/books?id=DbnPAAAAMAAJ |title=Lectures on Theory of Approximation |year=1962}}</ref> Several [[minimax approximation algorithm]]s are available, the most common being the [[Remez algorithm]]. ...

In mathematics, '''Arakelyan's theorem''' is a generalization of [[Mergelyan's ...connected.<ref>{{cite book|last1=Gardiner|first1=Stephen J.|title=Harmonic approximation|url=https://archive.org/details/harmonicapproxim00gard_738|url-access=limit ...

{{Short description|In approximation theory, a converse to Jackson's theorem}} ...}</ref> The first results of this type were proved by [[Sergei Bernstein]] in 1912.<ref>{{cite book|last=Bernstein|first=S.N.|author-link=Sergey Bernstei ...

...general functions by functions of special form, such as [[polynomial]]s. In more recent work, the convergence of a sequence of operators is studied: th ...sequence of real numbers tending to zero. Then there exists a point ''x'' in ''X'' such that the distance of ''x'' to ''V''_''i'' is exactly < ...

...Arthur Rosenthal]] and has been widely applied, particularly in [[operator theory]]. ...continuous function on ''K'' can be uniformly approximated by a polynomial in <math>z</math> and <math>\overline{z}</math>. ...

...oximated by another kind. Specifically it tells us that we can get a good approximation to irrational numbers that are not quadratic by using either [[quadratic ir ...''y'', and ''z'' to be the coefficients of its [[minimal polynomial (field theory)|minimal polynomial]]. If α is rational we will have ''x''&nbsp;=&nbsp;0. ...

...t description|Theorem in number theory that gives a bound on a Diophantine approximation}} {{About|a theorem in number theory||Hurwitz's theorem (disambiguation){{!}}Hurwitz's theorem}} ...

...SP/Ones classification theorems give information about the complexity of [[approximation algorithm|approximating]] an optimal solution to a problem defined by ''S'' ...s. The ''Max Ones problem'' is to maximize the number of boolean variables in ''S'' that are set to 1 under the restriction that all clauses are satisfie ...

...lm Wirtinger]] in 1932 in connection with some problems of [[approximation theory]]. This theorem gives the representation formula for the [[Holomorphic func }}</ref> contains the following theorem presented also in [[Joseph L. Walsh]]'s well-known monograph ...

...ml.org/doc/149665}}</ref><ref>{{cite journal|author=Walsh, J. L.|title=The approximation of harmonic functions by harmonic polynomials and by harmonic rational func ...ly]] on <math>\partial{K}</math> by (real-valued) [[harmonic polynomial]]s in the real variables {{math|x}} and {{math|y}}.<ref>{{cite book|author=Gameli ...

...ian)|János Komlós]], [[Gábor Tusnády]], and [[Péter Major]], who proved it in 1975. ==Theory== ...

...te book|title=Fixed Point Theorems with Applications to Economics and Game Theory|last=Border|first=Kim C.|publisher=Cambridge University Press|year=1989|isb : <math>\forall x \in X: \,\,\, f(x) \in F(x) \,.</math> ...

...urnal|first=Dorin|last= Popescu|title= General Néron desingularization and approximation|journal=Nagoya Mathematical Journal|volume= 104 |year=1986|pages= 85–115|m ...ournal = [[Journal of Algebra]] | mr = 1935511 | pages = 489–515 | title = Approximation of versal deformations | url = https://math.stanford.edu/~conrad/papers/app ...

...version of the theorem states that, if a finite set of red and blue points in the [[Euclidean plane]] has the property that, for every four points, there {{quote|If sheep and goats are grazing in a field and for every four animals there exists a line separating the sheep ...

...rican Mathematical Society| year=1965}}</ref> a simplified proof was given in 1976 by A. Pinkus.<ref name="Pinkus 1976">{{cite journal|last=Pinkus|first= Define a ''signed partition'' as a partition in which each subinterval <math>i</math> has an associated sign <math>\delta_i ...

...math>f(X^n)\subseteq Y^n</math> for all ''n''. The content of the cellular approximation theorem is then that any continuous map ''f'' : ''X'' → ''Y'' between CW-co ...</math>, the map ''f'' is already cellular on ''e''^''n'', since in this case only cells of the ''n''-skeleton of ''Y'' meets ''f''(''e''<sup>' ...

{{short description|Mathematical propositions in network flow theory}} ...nimum cut are not necessarily equal. Instead, approximate max-flow min-cut theorems provide bounds on how close the maximum flow can get to the minimum cut, wi ...

...Bergman space and hence an explicit form of the [[Bergman kernel]], which in turn yields an explicit [[Riemann mapping theorem|Riemann mapping function] ...nel theorem]] ''f''_''n''(''z'') converges uniformly on compacta in Ω to ''z''.<ref>See: ...

In [[mathematical analysis]], '''Krein's condition''' provides a necessary and \quad a_k \in \mathbb{C}, \, \lambda_k \geq 0 \right\},</math> ...

{{Short description|Uniform approximation theorem in mathematics}} In mathematics, especially the theory of [[Function of several complex variables|several complex variables]], the ...