Hiroshi Murakami
Abstract
The continued fraction expansion method is a fast solver to find a rational number in a given real interval whose denominator is the smallest. A simple implementation of the CF expansion method which uses floating point numbers as real numbers has a possibility to give a wrong answer by the effect of numerical round-off errors. In this paper, we show a modification of the algorithm of the CF expansion method so that it uses floating point (FP) intervals as replacements of real numbers. By this modified algorithm, the answer is obtained only when its correctness is guaranteed and the possibility to give a wrong answer is eliminated.
- Hiroshi Murakami. A continued fraction type method to find a rational number in a given closed interval whose denominator is minimal. ACM Communications in Computer Algebra, Vol 43,No.3,Issue 169, pp.88--90,Sep. 2009. Google Scholar
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