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DTSTAMP:20250822T115808Z
LOCATION:Room 5.2D02
DTSTART;TZID=Europe/Stockholm:20250618T093000
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UID:submissions.pasc-conference.org_PASC25_sess106_msa102@linklings.com
SUMMARY:Fast and Accurate Algorithm Efficiently Using FMA for Matrix Multi
 plication
DESCRIPTION:KATSUHISA OZAKI (Shibaura Institute of Technology) and Toru Ko
 izumi (Nagoya Institute of Technology)\n\nWe introduce a new algorithm for
  high-precision computations of matrix multiplication. While hardware-supp
 orted floating-point operations are fast, they suffer from rounding errors
  due to their finite precision. When the accuracy of computed results is n
 ot satisfactory, high-precision computation may be considered. One option 
 is to use multi-precision arithmetic, such as MPFR. However, if extending 
 the range of the exponent part is unnecessary, an alternative is to repres
 ent numbers as the sum of floating-point numbers and perform operations on
  those sums. Examples include pair arithmetic by Lange and Rump and double
 -word arithmetic by Bailey.\nIn this talk, we introduce an algorithm that 
 leverages this structure for fused multiply-add operations and applies it 
 to matrix multiplication. As a result, we have designed a computational me
 thod that is less costly than pair arithmetic or double-word arithmetic, a
 llowing for a slight degradation in accuracy. Finally, we demonstrate the 
 performance of the proposed method through numerical experiments. Addition
 ally, we compare the performance of the proposed method with the GEMM-base
 d emulation method known as the Ozaki scheme.\n\nDomain: Computational Met
 hods and Applied Mathematics\n\nSession Chair: Mantas Mikaitis (University
  of Leeds)\n\n
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