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extreme-value theorem

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  • Extreme value theorem — This article is about continuous functions in analysis. For statistical theorems about the largest observation in a sequence of random variables, see extreme value theory. A continuous function ƒ(x) on the closed interval [a,b] showing the… …   Wikipedia

  • Extreme value — The largest and the smallest element of a set are called extreme values, absolute extrema, or extreme records.For a differentiable function f, if f(x 0) is an extreme value for the set of all values f(x), and if x 0 is in the interior of the… …   Wikipedia

  • Extreme value theory — is a branch of statistics dealing with the extreme deviations from the median of probability distributions. The general theory sets out to assess the type of probability distributions generated by processes. Extreme value theory is important for… …   Wikipedia

  • Mean value theorem — For the theorem in harmonic function theory, see Harmonic function#Mean value property. Topics in Calculus Fundamental theorem Limits of functions Continuity Mean value theorem Differential calculus  Derivative Change of variables …   Wikipedia

  • Generalized extreme value distribution — Probability distribution name =Generalized extreme value type =density pdf cdf parameters =mu in [ infty,infty] , location (real) sigma in (0,infty] , scale (real) xiin [ infty,infty] , shape (real) support =x>mu sigma/xi,;(xi > 0) x …   Wikipedia

  • Rolle's theorem — In calculus, a branch of mathematics, Rolle s theorem essentially states that a differentiable function, which attains equal values at two points, must have a stationary point somewhere between them.tandard version of the theoremIf a real valued… …   Wikipedia

  • Singular value decomposition — Visualization of the SVD of a 2 dimensional, real shearing matrix M. First, we see the unit disc in blue together with the two canonical unit vectors. We then see the action of M, which distorts the disk to an ellipse. The SVD decomposes M into… …   Wikipedia

  • Darboux's theorem (analysis) — Darboux s theorem is a theorem in real analysis, named after Jean Gaston Darboux. It states that all functions that result from the differentiation of other functions have the intermediate value property: the image of an interval is also an… …   Wikipedia

  • Weierstrass theorem — Several theorems are named after Karl Weierstrass. These include: *The Weierstrass approximation theorem, also known as the Stone Weierstrauss theorem *The Bolzano Weierstrass theorem, which ensures compactness of closed and bounded sets in R n… …   Wikipedia

  • Maximum theorem — The maximum theorem provides conditions for the continuity of an optimized function and the set of its maximizers as a parameter changes. The statement was first proven by Claude Berge in 1959[1]. The theorem is primarily used in mathematical… …   Wikipedia

  • Inverse function theorem — In mathematics, specifically differential calculus, the inverse function theorem gives sufficient conditions for a function to be invertible in a neighborhood of a point in its domain. The theorem also gives a formula for the derivative of the… …   Wikipedia

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