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Dev Days 1: Exact Linear Algebra

• Michael Abshoff
• Martin Albrecht
• Nick Alexander
• Gregory Bard
• Rob Beezer
• Tom Boothby
• Craig Citro
• Burcin Erocal
• Robert Miller (especially sparse GF(2))
• David Roe (p-adic linear algebra?)
• Arne Storjohann
• William Stein
• Ralf-Philipp Weinmann

Dense GF(2)

• implement LQUP decomposition [Clement, Martin]
  • implement LQUP routine [Clement]
  • implement TRSM routine [Clement]
  • implement efficient column swaps/rotations [Martin]
    • SSE2 might help a lot here
  • implement memory efficient mzd_addmul_strassen [Martin]
    • See Clement's et al. paper on memory efficient Strassen-Winograd
• implement Arne's asymptotically fast elimination algorithm [Martin]
• implement multi-core multiplication with optimal speed-up
  • OpenMP seems to be nice and easy
  • 2 cores probably main target, but think about 4 cores too
• improve efficiency of M4RM
  • try 7 instead of 8 Gray code tables to leave room for the actual matrix in L1
  • try to fit three matrices rather than two into L2 or understand why it works so good for two
  • detect L1/L2 cache sizes at runtime and choose optimal parameters for them
  • implement Bill's half table idea and benchmark it

Sparse GF(2) (and other small finite fields)

• Sparse Reduced Echelon form (RPW)
  • Sparse Elimination:

    • improve LinBox gauss-domain

    • eclib sparse elimination
    • ....
• ....

Hermite Normal Form

• new algorithm (Storjohann)