Arnold Schönhage
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Arnold Schönhage (born 1 December 1934 in Lockhausen, now
Bad Salzuflen Bad Salzuflen () is a town and thermal spa resort in the Lippe district of North Rhine-Westphalia, Germany. At the end of 2013, it had 52,121 inhabitants. Geography Bad Salzuflen lies on the eastern edge of the Ravensberg Basin, at the confluenc ...
) is a German
mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...
and
computer scientist A computer scientist is a scientist who specializes in the academic study of computer science. Computer scientists typically work on the theoretical side of computation. Although computer scientists can also focus their work and research on ...
. Schönhage was professor at the Rheinische Friedrich-Wilhelms-Universität, Bonn, and also in
Tübingen Tübingen (; ) is a traditional college town, university city in central Baden-Württemberg, Germany. It is situated south of the state capital, Stuttgart, and developed on both sides of the Neckar and Ammer (Neckar), Ammer rivers. about one in ...
and
Konstanz Konstanz ( , , , ), traditionally known as Constance in English, is a college town, university city with approximately 83,000 inhabitants located at the western end of Lake Constance in the Baden-Württemberg state of south Germany. The city ho ...
. Together with Volker Strassen, he developed the Schönhage–Strassen algorithm for the multiplication of large numbers that has a runtime of '' O''(''N'' log ''N'' log log ''N''). For many years, this was the fastest way to multiply large integers, although Schönhage and Strassen predicted that an algorithm with a run-time of N(logN) should exist. In 2019, Joris van der Hoeven and David Harvey finally developed an algorithm with this runtime, proving that Schönhage's and Strassen's prediction had been correct. Schönhage designed and implemented together with Andreas F. W. Grotefeld and Ekkehart Vetter a multitape
Turing machine A Turing machine is a mathematical model of computation describing an abstract machine that manipulates symbols on a strip of tape according to a table of rules. Despite the model's simplicity, it is capable of implementing any computer algori ...
, called TP, in software. The machine is programmed in TPAL, an
assembler language In computing, assembly language (alternatively assembler language or symbolic machine code), often referred to simply as assembly and commonly abbreviated as ASM or asm, is any low-level programming language with a very strong correspondence bet ...
. They implemented numerous numerical algorithms, including the Schönhage–Strassen algorithm, on this machine. The Odlyzko–Schönhage algorithm from 1988 is regularly used in research on the
Riemann zeta function The Riemann zeta function or Euler–Riemann zeta function, denoted by the Greek letter (zeta), is a mathematical function of a complex variable defined as \zeta(s) = \sum_^\infty \frac = \frac + \frac + \frac + \cdots for and its analytic c ...
.


References


External links


Homepage with list of publications


{{DEFAULTSORT:Schonhage, Arnold 1934 births Living people People from Bad Salzuflen German computer scientists Approximation theorists People from the Free State of Lippe 20th-century German mathematicians 21st-century German mathematicians Academic staff of the University of Bonn Academic staff of the University of Tübingen Academic staff of the University of Konstanz University of Cologne alumni