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Schonhage-Strassen Algorithm

Schonhage-Strassen Algorithm


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About the Book

High Quality Content by WIKIPEDIA articles! The Schonhage-Strassen algorithm is an asymptotically fast multiplication algorithm for large integers. It was developed by Arnold Schonhage and Volker Strassen in 1971. The run-time bit complexity is, in Big O notation, O(N log N log log N), while the arithmetic complexity is O(N log N). The algorithm uses recursive Fast Fourier transforms in rings with 22n + 1 elements, a specific type of number theoretic transform. The Schonhage-Strassen algorithm was the asymptotically fastest multiplication method known from 1971 to 2007 when a new method, Furer's algorithm, was announced with lower asymptotic complexity; however, Furer's algorithm currently only achieves an advantage for astronomically large values and is not used in practice. In practice the Schonhage-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).


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Product Details
  • ISBN-13: 9786131157929
  • Publisher: Betascript Publishing
  • Publisher Imprint: Betascript Publishing
  • Height: 152 mm
  • Weight: 145 gr
  • ISBN-10: 6131157928
  • Publisher Date: 10 Aug 2010
  • Binding: Paperback
  • Spine Width: 6 mm
  • Width: 229 mm


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