Numerical Linear Algebra
where the algebra stops being the arithmetic
Ladder

Structured spectrum — 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. -5-3.20611-1.412210.3816782.175573.969460log₁₀ |λ||λ| = 1λλ′ = 1, in the algebrapairs6decades of spectrum9.6pairing error, general3.3·10⁻⁹pairing error, structured2.2·10⁻¹⁶a symmetry the solver never knew aboutand the half of the answer it decides

    A spectrum that comes in reciprocal pairs

    A palindromic quadratic reads the same backwards, so λ is an eigenvalue exactly when 1/λ is. A general solver discards that, computes the large half of the spectrum perfectly and the small half to seven digits — and the small half is a division away from being perfect too.

    rung 1 · polynomial

All ladders