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Am 24.08.2013 22:30, schrieb Vincent Lefevre:
On 2013-08-24 12:49:46 -0700, G. William (Bill) Walster wrote:As far as I can tell the only time when a case can be made that EDP is essential for interval computations is when all interval inputs are degenerate and therefore infinitely precise.Even in this case (and you want the tightest accuracy mode), EDP is not essential. You just need a correctly rounded dot product.
Vincent,a correctly rounded dot product suffices for many applications. But there are many other applications where an EDP is needed. If you check for the EDP in the XSC-languages Pascal-XSC, ACRITH-XSC of IBM, and C-XSC or in the corresponding toolbox volumes (see the references of my mail of August 7, 2013) you will find that it appears all over. If you need a particular reference, just read the section "Verified Solution of Systems of Linear Equations" in my book "Computer Arithmetic and Validity". In earlier mails I repeatedly mentioned two other nice applications: Rump's mehtod for numerical verification of arbitrarily ill-conditioned linear systems, or multiple precision interval arithmetic and applications in my book.
Best regards Ulrich -- Karlsruher Institut für Technologie (KIT) Institut für Angewandte und Numerische Mathematik D-76128 Karlsruhe, Germany Prof. Ulrich Kulisch Telefon: +49 721 608-42680 Fax: +49 721 608-46679 E-Mail:ulrich.kulisch@xxxxxxx www.kit.edu www.math.kit.edu/ianm2/~kulisch/ KIT - Universität des Landes Baden-Württemberg und nationales Großforschungszentrum in der Helmholtz-Gesellschaft