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Well, the Vienna Proposal states: | If xx=[l,u] is compact, m and r shall have the values defined by | set round up | r = 0.5*(u-l);m=l+r.
That formula is due to Prof. Oishi from Waseda university, Tokyo. See http://www.ti3.tu-harburg.de/paper/rump/OiRu02.pdf It guarantees that m-r <= l and u<=m+r so that the midpoint-radius conversion is an inclusion of the original interval. This formula is used in many places in INTLAB. In particular it is used for interval matrix-matrix multiplication. Performing this using midpoint-radius representation speeds up computation by orders of magnitude. The price is an overestimation of the result by a worst case factor 1.5 in radius. If the radii of the inputs are small, the overestimation is negligible. For details see http://www.ti3.tu-harburg.de/paper/rump/Ru99b.pdf Best wishes Siegfried M. Rump -- ===================================================== Prof. Dr. Siegfried M. Rump Institute for Reliable Computing Hamburg University of Technology Schwarzenbergstr. 95 21071 Hamburg Germany phone +49 40 42878 3027 fax +49 40 42878 2489 http://www.ti3.tu-harburg.de and Visiting Professor at Waseda University Faculty of Science and Engineering Shinjuku Lambdax Bldg. 902 2-4-12 Okubo, Shinjuku-ku Tokyo 169-0072 Japan phone/fax in Japan +81 3 5286 3414