Numerical Linear Algebra
where the algebra stops being the arithmetic
Ladder

Interior point conditioning — 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. -14-12-10-8-6-4-2010⁻¹⁷10⁻¹³10⁻⁹10⁻⁵10⁻¹10³10⁷10¹¹10¹⁵log₁₀ μ — the barrier parametercondition number, and relative errorκ₂, condensedκ₂, augmentederror, condensederror, augmentedagainst a BigInt answerκ₂ augmented, μ = 10⁻¹⁴3·10¹⁵its relative error10⁻¹⁵κ₂ condensed2.4·10¹⁶its relative error0.31the same step, written two waysand only one of them is solvable

    A condition number sent to infinity

    An interior-point method manufactures an ill-conditioned matrix on every iteration, deliberately, because the separating of a diagonal is how it discovers which constraints are active. Written one way the answer keeps fifteen digits at a condition number of 3·10¹⁵. Written the other way — the way almost every code writes it — it has none left.

    rung 1 · constraint

All ladders