Interval Analysis: A New Tool for Applied Mathematics.
Technical summary rept.,
WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
Pagination or Media Count:
Interval arithmetic has been found to be useful in numerical analysis as an automatic means to bound data, truncation, and roundoff errors in computations. Now that the speed of microprogrammed interval arithmetic approaches that of standard floating-point operations, a wider range of application to engineering and other problems has become feasible. Since, in many practical situations, data are only known to lie within intervals and only ranges of values are sought as satisfactory answers, straightforward interval computation can yield the desired results. Examples of this type of application are worst-case analysis of the stability of structures and the performance of electrical circuits. The recently developed theory of integration of interval functions also bears directly on the problems of solution of integral equations and the minimization of functionals defined in terms of integrals. Since certain chaotic phenomena, such as catastrophes and turbulence, are difficult to describe by single-valued functions, the introduction of interval functions and the corresponding analysis may lead to simpler models which will yield results of accuracy satisfactory for practical purposes.
- Theoretical Mathematics