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- Prefix_sum abstract "In computer science, the prefix sum, scan, or cumulative sum of a sequence of numbers x0, x1, x2, ... is a second sequence of numbers y0, y1, y2, ..., the sums of prefixes (running totals) of the input sequence:y0 = x0y1 = x0 + x1y2 = x0 + x1+ x2...For instance, the prefix sums of the natural numbers are the triangular numbers:Prefix sums are trivial to compute in sequential models of computation, by using the formula yi = yi − 1 + xi to compute each output value in sequence order. However, despite their ease of computation, prefix sums are a useful primitive in certain algorithms such as counting sort, and they form the basis of the scan higher-order function in functional programming languages. Prefix sums have also been much studied in parallel algorithms, both as a test problem to be solved and as a useful primitive to be used as a subroutine in other parallel algorithms.Abstractly, a prefix sum requires only a binary associative operator ⊕, making it useful for many applications from calculating well-separated pair decompositions of points to string processing. Mathematically, the operation of taking prefix sums can be generalized from finite to infinite sequences; in that context, a prefix sum is known as a partial sum of a series. Prefix summation or partial summation form linear operators on the vector spaces of finite or infinite sequences; their inverses are finite difference operators.".
- Prefix_sum thumbnail Prefix_sum_16.svg?width=300.
- Prefix_sum wikiPageID "6109308".
- Prefix_sum wikiPageLength "15004".
- Prefix_sum wikiPageOutDegree "51".
- Prefix_sum wikiPageRevisionID "680191733".
- Prefix_sum wikiPageWikiLink Adder_(electronics).
- Prefix_sum wikiPageWikiLink Addition.
- Prefix_sum wikiPageWikiLink Alexandre-Théophile_Vandermonde.
- Prefix_sum wikiPageWikiLink Array_data_structure.
- Prefix_sum wikiPageWikiLink Associative_property.
- Prefix_sum wikiPageWikiLink C++.
- Prefix_sum wikiPageWikiLink Category:Concurrent_algorithms.
- Prefix_sum wikiPageWikiLink Category:Higher-order_functions.
- Prefix_sum wikiPageWikiLink Computer_science.
- Prefix_sum wikiPageWikiLink Counting_sort.
- Prefix_sum wikiPageWikiLink Divided_difference.
- Prefix_sum wikiPageWikiLink Divided_differences.
- Prefix_sum wikiPageWikiLink Euler_tour.
- Prefix_sum wikiPageWikiLink Eulerian_path.
- Prefix_sum wikiPageWikiLink Exclusive_or.
- Prefix_sum wikiPageWikiLink Factorial.
- Prefix_sum wikiPageWikiLink Finite_difference.
- Prefix_sum wikiPageWikiLink Fold_(higher-order_function).
- Prefix_sum wikiPageWikiLink Functional_programming.
- Prefix_sum wikiPageWikiLink GPU.
- Prefix_sum wikiPageWikiLink Graphics_processing_unit.
- Prefix_sum wikiPageWikiLink Gray_code.
- Prefix_sum wikiPageWikiLink Haskell_(programming_language).
- Prefix_sum wikiPageWikiLink Hermite_interpolation.
- Prefix_sum wikiPageWikiLink Higher-order_function.
- Prefix_sum wikiPageWikiLink Higher_order_function.
- Prefix_sum wikiPageWikiLink Histogram.
- Prefix_sum wikiPageWikiLink Integer_sorting.
- Prefix_sum wikiPageWikiLink Linear_map.
- Prefix_sum wikiPageWikiLink Linear_operator.
- Prefix_sum wikiPageWikiLink Linked_list.
- Prefix_sum wikiPageWikiLink List_ranking.
- Prefix_sum wikiPageWikiLink Majority_function.
- Prefix_sum wikiPageWikiLink Message_Passing_Interface.
- Prefix_sum wikiPageWikiLink Natural_number.
- Prefix_sum wikiPageWikiLink Newton_form.
- Prefix_sum wikiPageWikiLink Newton_polynomial.
- Prefix_sum wikiPageWikiLink Parallel_algorithm.
- Prefix_sum wikiPageWikiLink Parallel_random-access_machine.
- Prefix_sum wikiPageWikiLink Parallel_random_access_machine.
- Prefix_sum wikiPageWikiLink Partial_sum.
- Prefix_sum wikiPageWikiLink Polynomial_interpolation.
- Prefix_sum wikiPageWikiLink Prefix_(computer_science).
- Prefix_sum wikiPageWikiLink Radix_sort.
- Prefix_sum wikiPageWikiLink Running_total.
- Prefix_sum wikiPageWikiLink Series_(mathematics).
- Prefix_sum wikiPageWikiLink Sorting_network.
- Prefix_sum wikiPageWikiLink Substring.
- Prefix_sum wikiPageWikiLink Summation.
- Prefix_sum wikiPageWikiLink Tree_(graph_theory).
- Prefix_sum wikiPageWikiLink Triangular_number.
- Prefix_sum wikiPageWikiLink Vandermonde.
- Prefix_sum wikiPageWikiLink Vector_space.
- Prefix_sum wikiPageWikiLink Well-separated_pair_decomposition.
- Prefix_sum wikiPageWikiLink File:Prefix_sum_16.svg.
- Prefix_sum wikiPageWikiLinkText "'scan'".
- Prefix_sum wikiPageWikiLinkText "Prefix sum".
- Prefix_sum wikiPageWikiLinkText "parallel prefix sum".
- Prefix_sum wikiPageWikiLinkText "prefix sum".
- Prefix_sum wikiPageWikiLinkText "scan".
- Prefix_sum hasPhotoCollection Prefix_sum.
- Prefix_sum title "Cumulative Sum".
- Prefix_sum urlname "CumulativeSum".
- Prefix_sum wikiPageUsesTemplate Template:Math.
- Prefix_sum wikiPageUsesTemplate Template:Mathworld.
- Prefix_sum wikiPageUsesTemplate Template:Mvar.
- Prefix_sum wikiPageUsesTemplate Template:Reflist.
- Prefix_sum subject Category:Concurrent_algorithms.
- Prefix_sum subject Category:Higher-order_functions.
- Prefix_sum type Article.
- Prefix_sum type Algorithm.
- Prefix_sum type Article.
- Prefix_sum type Function.
- Prefix_sum type Subroutine.
- Prefix_sum comment "In computer science, the prefix sum, scan, or cumulative sum of a sequence of numbers x0, x1, x2, ... is a second sequence of numbers y0, y1, y2, ..., the sums of prefixes (running totals) of the input sequence:y0 = x0y1 = x0 + x1y2 = x0 + x1+ x2...For instance, the prefix sums of the natural numbers are the triangular numbers:Prefix sums are trivial to compute in sequential models of computation, by using the formula yi = yi − 1 + xi to compute each output value in sequence order.".
- Prefix_sum label "Prefix sum".
- Prefix_sum sameAs Präfixsumme.
- Prefix_sum sameAs m.0fqj7x.
- Prefix_sum sameAs Q7239858.
- Prefix_sum sameAs Q7239858.
- Prefix_sum wasDerivedFrom Prefix_sum?oldid=680191733.
- Prefix_sum depiction Prefix_sum_16.svg.
- Prefix_sum isPrimaryTopicOf Prefix_sum.