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- Binary_splitting abstract "In mathematics, binary splitting is a technique for speeding up numerical evaluation of many types of series with rational terms. In particular, it can be used to evaluate hypergeometric series at rational points. Given a serieswhere pn and qn are integers, the goal of binary splitting is to compute integers P(a, b) and Q(a, b) such thatThe splitting consists of setting m = [(a + b)/2] and recursively computing P(a, b) and Q(a, b) from P(a, m), P(m, b), Q(a, m), and Q(m, b). When a and b are sufficiently close, P(a, b) and Q(a, b) can be computed directly from pa...pb and qa...qb.Binary splitting requires more memory than direct term-by-term summation, but is asymptotically faster since the sizes of all occurring subproducts are reduced. Additionally, whereas the most naive evaluation scheme for a rational series uses a full-precision division for each term in the series, binary splitting requires only one final division at the target precision; this is not only faster, but conveniently eliminates rounding errors. To take full advantage of the scheme, fast multiplication algorithms such as Toom–Cook and Schönhage–Strassen must be used; with ordinary O(n2) multiplication, binary splitting may render no speedup at all or be slower.Since all subdivisions of the series can be computed independently of each other, binary splitting lends well to parallelization and checkpointing.In a less specific sense, binary splitting may also refer to any divide and conquer algorithm that always divides the problem in two halves.".
- Binary_splitting wikiPageExternalLink splitting.html.
- Binary_splitting wikiPageExternalLink algen.htm.
- Binary_splitting wikiPageExternalLink binsplit.pdf.
- Binary_splitting wikiPageID "4226251".
- Binary_splitting wikiPageRevisionID "544305709".
- Binary_splitting hasPhotoCollection Binary_splitting.
- Binary_splitting subject Category:Computer_arithmetic_algorithms.
- Binary_splitting type Abstraction100002137.
- Binary_splitting type Act100030358.
- Binary_splitting type Activity100407535.
- Binary_splitting type Algorithm105847438.
- Binary_splitting type ArbitraryPrecisionAlgorithms.
- Binary_splitting type Event100029378.
- Binary_splitting type Procedure101023820.
- Binary_splitting type PsychologicalFeature100023100.
- Binary_splitting type Rule105846932.
- Binary_splitting type YagoPermanentlyLocatedEntity.
- Binary_splitting comment "In mathematics, binary splitting is a technique for speeding up numerical evaluation of many types of series with rational terms. In particular, it can be used to evaluate hypergeometric series at rational points. Given a serieswhere pn and qn are integers, the goal of binary splitting is to compute integers P(a, b) and Q(a, b) such thatThe splitting consists of setting m = [(a + b)/2] and recursively computing P(a, b) and Q(a, b) from P(a, m), P(m, b), Q(a, m), and Q(m, b).".
- Binary_splitting label "Binary splitting".
- Binary_splitting label "Scindage binaire".
- Binary_splitting label "تفرع ثنائي".
- Binary_splitting sameAs Scindage_binaire.
- Binary_splitting sameAs m.0bqzwk.
- Binary_splitting sameAs Q584783.
- Binary_splitting sameAs Q584783.
- Binary_splitting sameAs Binary_splitting.
- Binary_splitting wasDerivedFrom Binary_splitting?oldid=544305709.
- Binary_splitting isPrimaryTopicOf Binary_splitting.