Arnold Schönhage
Encyclopedia
Arnold Schönhage is a mathematician
and computer scientist
and Professor Emeritus at Rheinische Friedrich-Wilhelms-Universität, Bonn
. He was also professor in Tübingen
and Konstanz
. Schönhage now lives near Bonn
, Germany
.
Schönhage together with Volker Strassen
developed the Schönhage–Strassen algorithm for fast integer multiplication that has a run-time of O
(N log N log log N).
Schönhage designed and implemented together with Andreas F. W. Grotefeld and Ekkehart Vetter a multitape Turing machine
, called TP, in software. The machine is programmed in TPAL, an assembler language. They implemented numerous numerical algorithms including the Schönhage–Strassen algorithm on this machine.
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
and computer scientist
Computer scientist
A computer scientist is a scientist who has acquired knowledge of computer science, the study of the theoretical foundations of information and computation and their application in computer systems....
and Professor Emeritus at Rheinische Friedrich-Wilhelms-Universität, Bonn
University of Bonn
The University of Bonn is a public research university located in Bonn, Germany. Founded in its present form in 1818, as the linear successor of earlier academic institutions, the University of Bonn is today one of the leading universities in Germany. The University of Bonn offers a large number...
. He was also professor in Tübingen
Tübingen
Tübingen is a traditional university town in central Baden-Württemberg, Germany. It is situated south of the state capital, Stuttgart, on a ridge between the Neckar and Ammer rivers.-Geography:...
and Konstanz
Konstanz
Konstanz is a university city with approximately 80,000 inhabitants located at the western end of Lake Constance in the south-west corner of Germany, bordering Switzerland. The city houses the University of Konstanz.-Location:...
. Schönhage now lives near Bonn
Bonn
Bonn is the 19th largest city in Germany. Located in the Cologne/Bonn Region, about 25 kilometres south of Cologne on the river Rhine in the State of North Rhine-Westphalia, it was the capital of West Germany from 1949 to 1990 and the official seat of government of united Germany from 1990 to 1999....
, Germany
Germany
Germany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...
.
Schönhage together with Volker Strassen
Volker Strassen
Volker Strassen is a German mathematician, a professor emeritus in the department of mathematics and statistics at the University of Konstanz.-Biography:Strassen was born on April 29, 1936, in Düsseldorf-Gerresheim....
developed the Schönhage–Strassen algorithm for fast integer multiplication that has a run-time of O
Big O notation
In mathematics, big O notation is used to describe the limiting behavior of a function when the argument tends towards a particular value or infinity, usually in terms of simpler functions. It is a member of a larger family of notations that is called Landau notation, Bachmann-Landau notation, or...
(N log N log log N).
Schönhage designed and implemented together with Andreas F. W. Grotefeld and Ekkehart Vetter a multitape Turing machine
Turing machine
A Turing machine is a theoretical device that manipulates symbols on a strip of tape according to a table of rules. Despite its simplicity, a Turing machine can be adapted to simulate the logic of any computer algorithm, and is particularly useful in explaining the functions of a CPU inside a...
, called TP, in software. The machine is programmed in TPAL, an assembler language. They implemented numerous numerical algorithms including the Schönhage–Strassen algorithm on this machine.
See also
- Odlyzko–Schönhage algorithm
- Schönhage's Storage Modification Machine (SMM) model