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When comparing MidRad methods with InfSup, Siegfried Rump wrote:The reason is first that matrix mid-rad IV-multiplication can use BLAS routines. Second it needs only 2 times to switch the rounding mode compared to (at best) nµ2 times for inf-sup multiplication.A good InfSup implementation would avoid the cost of rounding mode changes; the method used may be platform-specific. When directed operations (or pipes) are available, there is no switching. Otherwise one would most likely use sign reversal for one bound in the internal representation. Efficient multiplication might still be a challenge when intervals contain zero; I have not worked out the details...
On most of today's architectures there are no directed operations available. And the occurance of zero intervals is the whole point. Then mid-rad interval matrix multiplication is the only known way to use BLAS-3 routines. And this is unbeatably fast. Siegfried -- ===================================================== 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