Numerical Linear Algebra
where the algebra stops being the arithmetic
Ladder

Polynomial scaling — 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. 0246810⁻¹⁶10⁻¹³10⁻¹⁰10⁻⁷10⁻⁴10⁻¹log₁₀ γ, the change of unitsforward erroras writtenafter scalingone change of variableunscaled, worst0.0013scaled, worst1.7·10⁻¹³orders recovered10scaled coefficient spread4.5the answer was never the problemthe units were

    The scaling that buys ten orders

    Two lines computed from three norms, a change of variable that is exact in both directions, and the whole of the loss the previous essay measured comes back — flat, at every stop, because after scaling every stop is the same problem.

    rung 1 · polynomial

All ladders