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  2. Pairwise summation - Wikipedia

    en.wikipedia.org/wiki/Pairwise_summation

    For example, if the summands x i are uncorrelated random numbers with zero mean, the sum is a random walk and the condition number will grow proportional to . On the other hand, for random inputs with nonzero mean the condition number asymptotes to a finite constant as n → ∞ {\displaystyle n\to \infty } .

  3. Summation - Wikipedia

    en.wikipedia.org/wiki/Summation

    The summation of an explicit sequence is denoted as a succession of additions. For example, summation of [1, 2, 4, 2] is denoted 1 + 2 + 4 + 2, and results in 9, that is, 1 + 2 + 4 + 2 = 9. Because addition is associative and commutative, there is no need for parentheses, and the result is the same irrespective of the order of the summands ...

  4. List of sums of reciprocals - Wikipedia

    en.wikipedia.org/wiki/List_of_sums_of_reciprocals

    The sum of the reciprocals of the square numbers (the Basel problem) is the transcendental number ⁠ π 2 / 6 ⁠, or ζ(2) where ζ is the Riemann zeta function. The sum of the reciprocals of the cubes of positive integers is called Apéry's constant ζ (3) , and equals approximately 1.2021 .

  5. Condition number - Wikipedia

    en.wikipedia.org/wiki/Condition_number

    Condition numbers can also be defined for nonlinear functions, and can be computed using calculus.The condition number varies with the point; in some cases one can use the maximum (or supremum) condition number over the domain of the function or domain of the question as an overall condition number, while in other cases the condition number at a particular point is of more interest.

  6. Kahan summation algorithm - Wikipedia

    en.wikipedia.org/wiki/Kahan_summation_algorithm

    The algorithm performs summation with two accumulators: sum holds the sum, and c accumulates the parts not assimilated into sum, to nudge the low-order part of sum the next time around. Thus the summation proceeds with "guard digits" in c , which is better than not having any, but is not as good as performing the calculations with double the ...

  7. Infimum and supremum - Wikipedia

    en.wikipedia.org/wiki/Infimum_and_supremum

    The Minkowski sum of two sets and of real numbers is the set + := {+:,} consisting of all possible arithmetic sums of pairs of numbers, one from each set. The infimum and supremum of the Minkowski sum satisfy, if A ≠ ∅ ≠ B {\displaystyle A\neq \varnothing \neq B} inf ( A + B ) = ( inf A ) + ( inf B ) {\displaystyle \inf(A+B)=(\inf A ...

  8. Sumset - Wikipedia

    en.wikipedia.org/wiki/Sumset

    where is the set of square numbers. A subject that has received a fair amount of study is that of sets with small doubling , where the size of the set A + A {\displaystyle A+A} is small (compared to the size of A {\displaystyle A} ); see for example Freiman's theorem .

  9. Cesàro summation - Wikipedia

    en.wikipedia.org/wiki/Cesàro_summation

    In mathematical analysis, Cesàro summation (also known as the Cesàro mean [1] [2] or Cesàro limit [3]) assigns values to some infinite sums that are not necessarily convergent in the usual sense. The Cesàro sum is defined as the limit, as n tends to infinity, of the sequence of arithmetic means of the first n partial sums of the series.