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- Sch%C3%B6nhage%E2%80%93Strassen_algorithm abstract "The Schönhage–Strassen algorithm is an asymptotically fast multiplication algorithm for large integers. It was developed by Arnold Schönhage and Volker Strassen in 1971. The run-time bit complexity is, in Big O notation, O(n log n log log n) for two n-digit numbers. The algorithm uses recursive Fast Fourier transforms in rings with 22n + 1 elements, a specific type of number theoretic transform.The Schönhage–Strassen algorithm was the asymptotically fastest multiplication method known from 1971 until 2007, when a new method, Fürer's algorithm, was announced with lower asymptotic complexity; however, Fürer's algorithm currently only achieves an advantage for astronomically large values and is not used in practice.In practice the Schönhage–Strassen algorithm starts to outperform older methods such as Karatsuba and Toom–Cook multiplication for numbers beyond 2215 to 2217 (10,000 to 40,000 decimal digits). The GNU Multi-Precision Library uses it for values of at least 1728 to 7808 64-bit words (33,000 to 150,000 decimal digits), depending on architecture. There is a Java implementation of Schönhage–Strassen which uses it above 74,000 decimal digits.Applications of the Schönhage–Strassen algorithm include mathematical empiricism, such as the Great Internet Mersenne Prime Search and computing approximations of π, as well as practical applications such as Kronecker substitution, in which multiplication of polynomials with integer coefficients can be efficiently reduced to large integer multiplication; this is used in practice by GMP-ECM for Lenstra elliptic curve factorization.".
- Sch%C3%B6nhage%E2%80%93Strassen_algorithm thumbnail Integer_multiplication_by_FFT.svg?width=300.
- Sch%C3%B6nhage%E2%80%93Strassen_algorithm wikiPageID "1354446".
- Sch%C3%B6nhage%E2%80%93Strassen_algorithm wikiPageRevisionID "643192881".
- Sch%C3%B6nhage%E2%80%93Strassen_algorithm hasPhotoCollection Schönhage–Strassen_algorithm.
- Sch%C3%B6nhage%E2%80%93Strassen_algorithm subject Category:Computer_arithmetic_algorithms.
- Sch%C3%B6nhage%E2%80%93Strassen_algorithm subject Category:Multiplication.
- Sch%C3%B6nhage%E2%80%93Strassen_algorithm type Abstraction100002137.
- Sch%C3%B6nhage%E2%80%93Strassen_algorithm type Act100030358.
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- Sch%C3%B6nhage%E2%80%93Strassen_algorithm type Algorithm105847438.
- Sch%C3%B6nhage%E2%80%93Strassen_algorithm type ArbitraryPrecisionAlgorithms.
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- Sch%C3%B6nhage%E2%80%93Strassen_algorithm comment "The Schönhage–Strassen algorithm is an asymptotically fast multiplication algorithm for large integers. It was developed by Arnold Schönhage and Volker Strassen in 1971. The run-time bit complexity is, in Big O notation, O(n log n log log n) for two n-digit numbers.".
- Sch%C3%B6nhage%E2%80%93Strassen_algorithm label "Algorithme de Schönhage-Strassen".
- Sch%C3%B6nhage%E2%80%93Strassen_algorithm label "Algoritmo Schönhage-Strassen".
- Sch%C3%B6nhage%E2%80%93Strassen_algorithm label "Algoritmo di Schönhage-Strassen".
- Sch%C3%B6nhage%E2%80%93Strassen_algorithm label "Schönhage-Strassen-Algorithmus".
- Sch%C3%B6nhage%E2%80%93Strassen_algorithm label "Schönhage–Strassen algorithm".
- Sch%C3%B6nhage%E2%80%93Strassen_algorithm label "Метод умножения Шёнхаге — Штрассена".
- Sch%C3%B6nhage%E2%80%93Strassen_algorithm label "쇤하게-슈트라센 알고리즘".
- Sch%C3%B6nhage%E2%80%93Strassen_algorithm sameAs m.04w65t.
- Sch%C3%B6nhage%E2%80%93Strassen_algorithm sameAs Schönhage–Strassen_algorithm.
- Sch%C3%B6nhage%E2%80%93Strassen_algorithm wasDerivedFrom Schönhage–Strassen_algorithm?oldid=643192881.
- Sch%C3%B6nhage%E2%80%93Strassen_algorithm depiction Integer_multiplication_by_FFT.svg.
- Sch%C3%B6nhage%E2%80%93Strassen_algorithm isPrimaryTopicOf Schönhage–Strassen_algorithm.
