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DTSTAMP:20250822T115804Z
LOCATION:Room 5.2D02
DTSTART;TZID=Europe/Stockholm:20250618T090000
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UID:submissions.pasc-conference.org_PASC25_sess106_msa101@linklings.com
SUMMARY:Error Analysis of Matrix Multiplication with Narrow Range Floating
 -Point Arithmetic
DESCRIPTION:Theo Mary (CNRS) and Mantas Mikaitis (University of Leeds)\n\n
 High-performance computing hardware now supports many different floating-p
 oint formats, from 64 bits to only 4 bits. While the effects of reducing p
 recision in numerical linear algebra computations have been extensively st
 udied, some of these low precision formats also possess a very narrow rang
 e of representable values, meaning underflow and overflow are very likely.
  The goal of this article is to analyze the consequences of this narrow ra
 nge on the accuracy of matrix multiplication. We describe a simple scaling
  that can prevent overflow while minimizing underflow. We carry out an err
 or analysis to bound the underflow errors and show that they should remain
  dominated by the rounding errors in most practical scenarios. We also sho
 w that this conclusion remains true when multiword arithmetic is used. We 
 perform extensive numerical experiments that confirm that the narrow range
  of low precision arithmetics should not significantly affect the accuracy
  of matrix multiplication—provided a suitable scaling is used.\n\nDomain: 
 Computational Methods and Applied Mathematics\n\nSession Chair: Mantas Mik
 aitis (University of Leeds)\n\n
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