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  2. Numeric precision in Microsoft Excel - Wikipedia

    en.wikipedia.org/wiki/Numeric_precision_in...

    Excel maintains 15 figures in its numbers, but they are not always accurate; mathematically, the bottom line should be the same as the top line, in 'fp-math' the step '1 + 1/9000' leads to a rounding up as the first bit of the 14 bit tail '10111000110010' of the mantissa falling off the table when adding 1 is a '1', this up-rounding is not undone when subtracting the 1 again, since there is no ...

  3. 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 } .

  4. 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 ...

  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. Round-off error - Wikipedia

    en.wikipedia.org/wiki/Round-off_error

    There are two common rounding rules, round-by-chop and round-to-nearest. The IEEE standard uses round-to-nearest. Round-by-chop: The base-expansion of is truncated after the ()-th digit. This rounding rule is biased because it always moves the result toward zero.

  7. Matt Eberflus: Bears filing complaint with NFL that Packers ...

    www.aol.com/sports/matt-eberflus-bears-filing...

    Eberflus acknowledged that the Bears did a poor job of blocking, but believes that the Packers made illegal contact with long snapper Scott Daly on the play and wants the NFL to take a second look.

  8. Meghan Markle Says ‘Every Year It Gets Better’ When ... - AOL

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    Meghan Markle is opening up about her favorite holiday traditions with her family. In an interview with Marie Claire, the Duchess of Sussex, 43, said, “I love the holidays,” and said of Prince ...

  9. 30 Color Photos Photographers Took 100 Years Ago That Still ...

    www.aol.com/44-old-color-photos-showing...

    Image credits: Photoglob Zürich As evident from Niépce's and Maxwell's experiments, and as photographic process historian Mark Osterman told Bored Panda, the processes behind colored photographs ...

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