Rudi Klatte

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In the past interval analysis in the complex plane has used nearly exclusively the rectangular arithmeticRℂ resp. the circular arithmeticKℂ. Both arithmetics satisfy the inclusion property where the equality does not hold in general. To introduce new interval arithmetics it is therefore interesting to consider other subsets of the powerset ofℂ. This paper(More)
In addition to the integers, the real and complex numbers, the real segments (intervals) and complex segments as well as vectors and matrices over all of these comprise the fundamental data types in computation. We extendFORTRAN so that it accepts operands and operators for all of these types as primitives in expressions. We briefly review the spaces(More)
The well known concepts of screens and roundings are not always sufficient if one intends to derive statements in connection with the generation of arithmetics in spaces which are more general than those considered in [5]. In this paper the concept of the screen therefore is generalized to the concept of the (Si)-screen and instead of roundings the(More)
In ordered sets it is possible to show under certain assumptions two basic theorems concerning the cycle length of sequences of iterates generated by monotone operators. These results are applied to different iterative methods, where the conclusions are valid for the sequences of iterates produced by the numerical computations only, if the used computer(More)
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