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  2. Maximum and minimum - Wikipedia

    en.wikipedia.org/wiki/Maximum_and_minimum

    Finding global maxima and minima is the goal of mathematical optimization. If a function is continuous on a closed interval, then by the extreme value theorem, global maxima and minima exist. Furthermore, a global maximum (or minimum) either must be a local maximum (or minimum) in the interior of the domain, or must lie on the boundary of the ...

  3. Sample maximum and minimum - Wikipedia

    en.wikipedia.org/wiki/Sample_maximum_and_minimum

    The sample maximum and minimum are the least robust statistics: they are maximally sensitive to outliers.. This can either be an advantage or a drawback: if extreme values are real (not measurement errors), and of real consequence, as in applications of extreme value theory such as building dikes or financial loss, then outliers (as reflected in sample extrema) are important.

  4. Fermat's theorem (stationary points) - Wikipedia

    en.wikipedia.org/wiki/Fermat's_theorem...

    Fermat's theorem is central to the calculus method of determining maxima and minima: in one dimension, one can find extrema by simply computing the stationary points (by computing the zeros of the derivative), the non-differentiable points, and the boundary points, and then investigating this set to determine the extrema.

  5. Quasi-Newton method - Wikipedia

    en.wikipedia.org/wiki/Quasi-Newton_method

    In numerical analysis, a quasi-Newton method is an iterative numerical method used either to find zeroes or to find local maxima and minima of functions via an iterative recurrence formula much like the one for Newton's method, except using approximations of the derivatives of the functions in place of exact derivatives.

  6. Talk:Maximum and minimum - Wikipedia

    en.wikipedia.org/wiki/Talk:Maximum_and_minimum

    So a method of finding a global maximum (or minimum) is to look at all the local maxima (or minima) in the interior, and also look at the maxima (or minima) of the points on the boundary; and take the biggest (or smallest) one. Is there an efficient way to find the global maximum/minimum? Take for example the sine integral. It has an infinite ...

  7. Median - Wikipedia

    en.wikipedia.org/wiki/Median

    The median of a normal distribution with mean μ and variance σ 2 is μ. In fact, for a normal distribution, mean = median = mode. The median of a uniform distribution in the interval [a, b] is (a + b) / 2, which is also the mean. The median of a Cauchy distribution with location parameter x 0 and scale parameter y is x 0, the location parameter.

  8. Maximum-minimums identity - Wikipedia

    en.wikipedia.org/wiki/Maximum-minimums_identity

    In mathematics, the maximum-minimums identity is a relation between the maximum element of a set S of n numbers and the minima of the 2 n − 1 non-empty subsets of S. Let S = {x 1, x 2, ..., x n}. The identity states that

  9. Extreme value theorem - Wikipedia

    en.wikipedia.org/wiki/Extreme_value_theorem

    The extreme value theorem was originally proven by Bernard Bolzano in the 1830s in a work Function Theory but the work remained unpublished until 1930. Bolzano's proof consisted of showing that a continuous function on a closed interval was bounded, and then showing that the function attained a maximum and a minimum value.