### Werner Krandick (TRACS visitor, Paderborn, Germany)

#### Arithmetic for the real world

*Wednesday 23 October 1996 at 15.30, JCMB 6324*

##### Abstract

Many important problems in the exact sciences can be solved using exact
computation. The use of exact arithmetic, however, often leads to large
operands and unacceptable computing times. We propose to introduce rounded
computation steps in a controlled way. The accuracy of intermediate results
can be guaranteed by mathematical theorems, by self-validation, or by a
posteriori verification. Results can be rounded in a number of ways among
them floating point arithmetic. While retaining the mathematical integrity
of our methods we obtain dramatic reductions in average computing times.

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