[HN Gopher] New Breakthrough Brings Matrix Multiplication Closer...
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       New Breakthrough Brings Matrix Multiplication Closer to Ideal
        
       Author : bertman
       Score  : 16 points
       Date   : 2024-03-07 16:11 UTC (6 hours ago)
        
 (HTM) web link (www.quantamagazine.org)
 (TXT) w3m dump (www.quantamagazine.org)
        
       | Someone wrote:
       | As expected: closer, but not much closer. FTA: _"we give a new
       | bound of o <2.371866 [...]. Our result breaks the lower bound of
       | 2.3725"_
       | 
       | AFAIK the current theoretical lower bound still is 2, so that's
       | only 600-ish more such steps to get there.
       | 
       | On the positive side, I don't think anybody believes that 2 even
       | remotely is a tight bound.
        
       | sevagh wrote:
       | Can anybody who knows or understands better, how applicable is
       | this new technique to being used in a GEMM implementation in a
       | BLAS library in mainstream numerical libraries?
        
         | klyrs wrote:
         | It's been a great many years since I've touched this stuff but
         | two rules of thumb probably haven't changed in the meantime:
         | 
         | 1. in general, algorithms tend to slow down on small problems
         | in exchange for the asymptotic speedup -- so you probably don't
         | want to use this algorithm for anything that fits in memory (or
         | perhaps the solar system)
         | 
         | 2. in specific, asymptotically fast matrix multiplication tend
         | to be numerically unstable. So you probably don't want to use
         | this algorithm unless you're working with infinite precision.
        
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       (page generated 2024-03-07 23:01 UTC)