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Schönhage-Strassen Algorithm: Multiplication Algorithm, Integer, Arnold Schönhage, Volker Strassen, Bit Complexity -

English
2026-03-15
€156.58 €195.73

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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), while the arithmetic complexity is O(N ... Full description

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Description

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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), 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 Schönhage-Strassen algorithm was the asymptotically fastest multiplication method known from 1971 to 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).

More Information

Publisher OmniScriptum
Release year 2026
Cover type Softcover
EAN 9786131157929
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€156.58 €195.73