Numerical Linear Algebra
where the algebra stops being the arithmetic
Ladder

Ordering — the ladder

One essay so far against this idea. A ladder is the distinct arguments that stand against one idea, and this one has room to grow.
  1. natural1739reverse Cuthill–McKee1354minimum degree1026nested dissection1413matrix: 408 entries · dense factor: 10440bandwidth 12 · 4.26× the matrixbandwidth 12 · 3.32× the matrixbandwidth 123 · 2.51× the matrixbandwidth 108 · 3.46× the matrixn = 144, five-point stencilevery ordering fills in; none avoids it

    The order decides the memory

    Four elimination orderings on one matrix give factors of 1,739, 1,354, 1,413 and 1,026 entries. All four factorisations are exact, all four return the same answer, and the one with the better asymptotics is not the one that wins.

    rung 1 · sparsity

All ladders