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Dear intervalers, The enclosed paper presents and analyzes algorithms for interval matrix multiplication. Conversion from infsup to midrad representation is analyzed; also an optimal algorithm is given. In particular - Note that midrad matrix multiplication is significantly faster (factor 50 to 200 for n=1000) than the traditional and our Profil/Bias approach (Table 1.1). - The proposed conversion of infsup to midrad in Section 5.2 in the "Vienna proposal for interval standardization, Manuscript (2008)" set round up r = 0.5*(u-l);m=l+r. is not correct (see the remark following Theorem 3.6 in my paper). - The effect of overestimation in interval matrix multiplication is often small in practical applications such as the solution of linear systems (Section 5, in particular Table 5.10). The article will appear in "Numerical Algorithms". 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 3-4-1 Okubo, Shinjuku-ku Tokyo 169-8555 Japan phone/fax in Japan +81 3 5286 3330
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