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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.
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.
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.
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.
Abel's summation formula can be generalized to the case where is only assumed to be continuous if the integral is interpreted as a Riemann–Stieltjes integral: ∑ x < n ≤ y a n ϕ ( n ) = A ( y ) ϕ ( y ) − A ( x ) ϕ ( x ) − ∫ x y A ( u ) d ϕ ( u ) . {\displaystyle \sum _{x<n\leq y}a_{n}\phi (n)=A(y)\phi (y)-A(x)\phi (x)-\int _{x ...
In mathematics, a summation equation or discrete integral equation is an equation in which an unknown function appears under a summation sign. The theories of summation equations and integral equations can be unified as integral equations on time scales [ 1 ] using time scale calculus .
Borel summation requires that the coefficients do not grow too fast: more precisely, a n has to be bounded by n!C n+1 for some C. There is a variation of Borel summation that replaces factorials n! with (kn)! for some positive integer k, which allows the summation of some series with a n bounded by (kn)!C n+1 for some C.
The cover displays the mathematical symbol for summation, ... 657 pp (Second Edition) ISBN: 0-201-55802-5: OCLC: 29357079: Dewey Decimal. 510 20: LC Class: QA39.2 ...
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