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Universität Karlsruhe (TH)
Institut für Angewandte MathematikResearch Group
Computer Arithmetic and
Validated Numerics (CAVN)Head: Prof. Ulrich Kulisch
| Research |
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The Research Group for Computer Arithmetic and Validated Numerics (CAVN) within the Institute of Applied Mathematics (IAM) at the Universität Karlsruhe (TH) pursues research and development in the field of scientific computation. Enhanced computer arithmetic and validation techniques developed by the CAVN Group make the computer faster and more capable mathematically. Users are given tools which allow them to use the computer to assess the errors inevitably arising when conventional floating-point arithmetic is used. This is achieved by extending the customary computer arithmetic, and by the development and implementation of the extended arithmetic in hardware and software. Adoption and use of the new arithmetic has a strong influence on the architecture of computers, on programming languages, compilers, the runtime system, and the operating system. Thus, the CAVN Group pursues a broad spectrum of research activities:
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The XPA 3233,
developed by the CAVN Group. It computes very fast and absolutely error free. |
To put the new arithmetic into effect, the CAVN Group has developed and implemented extensions of certain programming languages, the so-called XSC-languages (eXtended Scientific Computing). Use of these extended languages allows the clear and elegant formulation of algorithms which guarantee the correctness of the computed result within close bounds. For many algorithms the computed interval constitutes proof of the existence and uniqueness of the exact result within the computed bounds.
Today the CAVN Group is considered a nucleus and center for worldwide activities in this field. Among its supporters is the state of Baden-Württemberg. So far, more than 50 graduates in mathematics, computer science, and engineering science have achieved doctoral or post-doctoral qualifications within the Group.
Research and development by the CAVN Group is done in close cooperation with business, industry, and science in many countries. The programming language Pascal-XSC and its compiler were jointly developed with Nixdorf, the ACRITH library of problem solving routines and the programming language ACRITH-XSC with IBM, and the programming environment ARITHMOS with Siemens. The CAVN Group maintains close relations with the computing industry, as well as with numerous businesses and research institutions in and outside of Germany. Participation in five significant EU projects to date has established a variety of collaboration within Europe.
Reports of research and development, libraries for the extended arithmetic, for elementary and special functions for real and interval data, the XSC-languages with compilers, and libraries of problem solving routines can all be obtained via the following web addresses:
http://www.uni-karlsruhe.de/~iam/cavn
ftp://ftp.iam.uni-karlsruhe.de
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The basic operations of validated numerics. |
| Teaching |
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The research results of the CAVN Group are offered to students of mathematics and of the engineering and the natural sciences through special lectures. A lecture cycle of three semester courses Validated Numerics I, II and III is given regularly. Starting from basics like automatic differentiation, mathematical fixed-point theorems, and interval arithmetic, enclosure methods are taught for all kinds of standard problems of numerical linear algebra and of differential and integral equations. In addition several special lectures are offered. Topics are, for instance, computer arithmetic, fundamentals of numerical computation, highly accurate approximation of mathematical functions in the computer, and methods of computer algebra.
With introductory lectures on informatics and algorithmic mathematics
the collaborators of the CAVN Group furnish the majority of students of
all departments with basic skills in computer programming. These lectures
are offered with exercises and practical training on the computers in the
computing center. They attract several hundred students each semester.
The contents of these lectures are constantly adapted to the dynamic development
of the computer market and of programming languages. At present these lectures
are given by means of the programming languages Pascal, Fortran, C, and
C++. The XSC-extensions of these languages are also presented. Thus, the
students are sensitized early to the problem of accuracy in computing.
| People |
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Research Group
Computer Arithmetic and Validated Numerics
Head: Prof. Dr. Ulrich Kulisch
Tel.: (+49) 721 - 608 - 26 80
Mail: ulrich.kulisch@math.uni-karlsruhe.de
All members of the CAVN Group collaborate in work over the entire
spectrum of activities. The main fields of study are:
URL: http://www.uni-karlsruhe.de/~iam/cavn
| Contact |
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scan 2000 in Karlsruhe
In September 2000 the Institute of Applied Mathematics and the Computing Center of the Universität Karlsruhe (TH) will host the prestigious SCAN-Congress: GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics. International experts in the fields of scientific computing, computer arithmetic, and validated numerics will meet at Karlsruhe on this occasion. The aim is to develop mathematics by means of the computer, and vice versa. Date: September 19 - 22, 2000
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Mailing address:
Institut für Angewandte Mathematik
Universität Karlsruhe (TH)
D-76128 KarlsruheVisitor address:
Institut für Angewandte Mathematik
Fakultätsgebäude Mathematik
Englerstraße 2
D-76131 KarlsruheTel.: (+49) 721 - 608 - 26 80
Fax: (+49) 721 - 69 52 83Off campus offices:
Kriegsstraße 45, 76133 Karlsruhe
Engesserstraße 2, 76131 Karlsruhe
