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  2. 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.

  3. Multi-document summarization - Wikipedia

    en.wikipedia.org/wiki/Multi-document_summarization

    Multi-document summarization is an automatic procedure aimed at extraction of information from multiple texts written about the same topic. The resulting summary report allows individual users, such as professional information consumers, to quickly familiarize themselves with information contained in a large cluster of documents.

  4. Summation by parts - Wikipedia

    en.wikipedia.org/wiki/Summation_by_parts

    In mathematics, summation by parts transforms the summation of products of sequences into other summations, often simplifying the computation or (especially) estimation of certain types of sums. It is also called Abel's lemma or Abel transformation , named after Niels Henrik Abel who introduced it in 1826.

  5. Automatic summarization - Wikipedia

    en.wikipedia.org/wiki/Automatic_summarization

    Abstractive summarization methods generate new text that did not exist in the original text. [12] This has been applied mainly for text. Abstractive methods build an internal semantic representation of the original content (often called a language model), and then use this representation to create a summary that is closer to what a human might express.

  6. Text summarization - Wikipedia

    en.wikipedia.org/?title=Text_summarization&...

    This page was last edited on 13 October 2021, at 13:46 (UTC).; Text is available under the Creative Commons Attribution-ShareAlike 4.0 License; additional terms may apply.

  7. Direct sum of modules - Wikipedia

    en.wikipedia.org/wiki/Direct_sum_of_modules

    In abstract algebra, the direct sum is a construction which combines several modules into a new, larger module. The direct sum of modules is the smallest module which contains the given modules as submodules with no "unnecessary" constraints, making it an example of a coproduct. Contrast with the direct product, which is the dual notion.

  8. Sums of powers - Wikipedia

    en.wikipedia.org/wiki/Sums_of_powers

    In mathematics and statistics, sums of powers occur in a number of contexts: . Sums of squares arise in many contexts. For example, in geometry, the Pythagorean theorem involves the sum of two squares; in number theory, there are Legendre's three-square theorem and Jacobi's four-square theorem; and in statistics, the analysis of variance involves summing the squares of quantities.

  9. Ramanujan summation - Wikipedia

    en.wikipedia.org/wiki/Ramanujan_summation

    Ramanujan summation is a technique invented by the mathematician Srinivasa Ramanujan for assigning a value to divergent infinite series.Although the Ramanujan summation of a divergent series is not a sum in the traditional sense, it has properties that make it mathematically useful in the study of divergent infinite series, for which conventional summation is undefined.

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