Edgar Kaucher
Edgar Kaucher | |
|---|---|
 | |
| Residence | Germany |
| Nationality | German |
| Alma mater | University of Karlsruhe |
| Known for | Kaucher interval arithmetic Emission Theory |
| Scientific career | |
| Fields | Mathematician |
| Institutions | University of Karlsruhe (Karlsruhe Institute of Technology) |
| Doctoral advisor | Ulrich W. Kulisch |
Edgar Kaucher is a German Mathematician and professor emeritus at the Institute for Applied and Numerical Mathematics of the University of Karlsruhe (now part of the Karlsruhe Institute of Technology). He is best known in numerical analysis for the extension of classical interval arithmetic that bears his name, commonly called Kaucher interval arithmetic. In his later years he took an interest in the interpretation of physical theories, which is the context in which his name appears among dissident scientists.
Biography
Kaucher completed his doctorate (Dr. rer. nat.) at the University of Karlsruhe in 1973 under the supervision of Ulrich W. Kulisch. His dissertation was titled Über metrische und algebraische Eigenschaften einiger beim numerischen Rechnen auftretender Räume ("On metric and algebraic properties of certain spaces arising in numerical computation"). After completing his doctorate he habilitated in mathematics and was appointed professor of mathematics at the University of Karlsruhe, working within the Institute for Applied and Numerical Mathematics. He remained active in teaching and research in mathematics and applied mathematics until his retirement around 2010. Among his own doctoral students were Rudolf Lohner, Günter Schumacher, Wolfram Klein and Alexander Dreyer.
Work
Kaucher's principal contribution is the algebraic extension of ordinary interval arithmetic that is now known as Kaucher interval arithmetic. Classical interval arithmetic operates only on "proper" intervals whose lower bound does not exceed the upper bound. Kaucher's construction, introduced in his 1973 dissertation and developed in subsequent papers, enlarges the set of intervals to include "improper" or directed intervals in which the bounds may be reversed. This completion turns the interval structure into an algebraic system with additional group-like properties, giving well-defined additive and multiplicative inverses that classical interval arithmetic lacks.
The resulting system, also referred to as extended, directed or modal interval arithmetic, has become one of the most widely used generalizations of classical interval arithmetic. It is applied in the guaranteed (verified) solution of interval linear systems, in inner and outer estimation of solution sets, and in tolerance, identification and control problems. Later authors have built software implementations and further theoretical justifications on top of his framework.
In his later years Kaucher took a private interest in questions of physics, including what he described as interpretation errors in physical theories and their constructive correction. This work, touching on topics such as Emission Theory and the foundations of relativity, is the reason his name is included among dissident scientists.