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  2. Pairwise summation - Wikipedia

    en.wikipedia.org/wiki/Pairwise_summation

    Pairwise summation is the default summation algorithm in NumPy [9] and the Julia technical-computing language, [10] where in both cases it was found to have comparable speed to naive summation (thanks to the use of a large base case).

  3. Goldbach's conjecture - Wikipedia

    en.wikipedia.org/wiki/Goldbach's_conjecture

    The Goldbach conjecture for practical numbers, a prime-like sequence of integers, was stated by Margenstern in 1984, [33] and proved by Melfi in 1996: [34] every even number is a sum of two practical numbers.

  4. Generalizations of Fibonacci numbers - Wikipedia

    en.wikipedia.org/wiki/Generalizations_of...

    That is, after two starting values, each number is the sum of the two preceding numbers. The Fibonacci sequence has been studied extensively and generalized in many ways, for example, by starting with other numbers than 0 and 1, by adding more than two numbers to generate the next number, or by adding objects other than numbers.

  5. Summation - Wikipedia

    en.wikipedia.org/wiki/Summation

    In mathematics, summation is the addition of a sequence of numbers, called addends or summands; the result is their sum or total.Beside numbers, other types of values can be summed as well: functions, vectors, matrices, polynomials and, in general, elements of any type of mathematical objects on which an operation denoted "+" is defined.

  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. Tacit programming - Wikipedia

    en.wikipedia.org/wiki/Tacit_programming

    Tacit programming, also called point-free style, ... is a program which computes the sum of a list of numbers. ... In the section on Python in this article, the ...

  8. Sum of two squares theorem - Wikipedia

    en.wikipedia.org/wiki/Sum_of_two_squares_theorem

    Therefore, the theorem states that it is expressible as the sum of two squares. Indeed, 2450 = 7 2 + 49 2. The prime decomposition of the number 3430 is 2 · 5 · 7 3. This time, the exponent of 7 in the decomposition is 3, an odd number. So 3430 cannot be written as the sum of two squares.

  9. 3-partition problem - Wikipedia

    en.wikipedia.org/wiki/3-partition_problem

    Therefore, the remaining 3-sets can be partitioned into two groups: n 3-sets containing the items u ij, and n 3-sets containing the items u ij '. In each matching pair of 3-sets, the sum of the two pairing items u ij +u ij ' is 44T+4, so the sum of the four regular items is 84T+4. Therefore, from the four regular items, we construct a 4-set in ...