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  2. Rate of convergence - Wikipedia

    en.wikipedia.org/wiki/Rate_of_convergence

    In some especially technical contexts, discretization methods' asymptotic rates and orders of convergence will be characterized by several scale parameters at once with the value of each scale parameter possibly affecting the asymptotic rate and order of convergence of the method with respect to the other scale parameters.

  3. Order of accuracy - Wikipedia

    en.wikipedia.org/wiki/Order_of_accuracy

    In numerical analysis, order of accuracy quantifies the rate of convergence of a numerical approximation of a differential equation to the exact solution. Consider u {\displaystyle u} , the exact solution to a differential equation in an appropriate normed space ( V , | | | | ) {\displaystyle (V,||\ ||)} .

  4. Convergence of random variables - Wikipedia

    en.wikipedia.org/wiki/Convergence_of_random...

    Convergence in distribution is the weakest form of convergence typically discussed, since it is implied by all other types of convergence mentioned in this article. However, convergence in distribution is very frequently used in practice; most often it arises from application of the central limit theorem .

  5. Big O in probability notation - Wikipedia

    en.wikipedia.org/wiki/Big_O_in_probability_notation

    The order in probability notation is used in probability theory and statistical theory in direct parallel to the big O notation that is standard in mathematics.Where the big O notation deals with the convergence of sequences or sets of ordinary numbers, the order in probability notation deals with convergence of sets of random variables, where convergence is in the sense of convergence in ...

  6. Halley's method - Wikipedia

    en.wikipedia.org/wiki/Halley's_method

    Halley's method is a numerical algorithm for solving the nonlinear equation f(x) = 0.In this case, the function f has to be a function of one real variable. The method consists of a sequence of iterations:

  7. Convergence of measures - Wikipedia

    en.wikipedia.org/wiki/Convergence_of_measures

    For (,) a measurable space, a sequence μ n is said to converge setwise to a limit μ if = ()for every set .. Typical arrow notations are and .. For example, as a consequence of the Riemann–Lebesgue lemma, the sequence μ n of measures on the interval [−1, 1] given by μ n (dx) = (1 + sin(nx))dx converges setwise to Lebesgue measure, but it does not converge in total variation.

  8. Order convergence - Wikipedia

    en.wikipedia.org/wiki/Order_convergence

    In mathematics, specifically in order theory and functional analysis, a filter in an order complete vector lattice is order convergent if it contains an order bounded subset (that is, a subset contained in an interval of the form [,]:= {:}) and if {: ⁡ ()} = {: ⁡ ()}, where ⁡ is the set of all order bounded subsets of X, in which case this common value is called the order limit of in . [1]

  9. Anderson acceleration - Wikipedia

    en.wikipedia.org/wiki/Anderson_acceleration

    However, the convergence of such a scheme is not guaranteed in general; moreover, the rate of convergence is usually linear, which can become too slow if the evaluation of the function is computationally expensive. [2] Anderson acceleration is a method to accelerate the convergence of the fixed-point sequence. [2]