Numerical Linear Algebra
where the algebra stops being the arithmetic
Ladder

Preconditioning — 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. 051015202530354010⁻¹¹10⁻⁹10⁻⁷10⁻⁵10⁻³10⁻¹iteration‖r‖ / ‖b‖plain CGIC(0) CGwhat the preconditioner didκ(A)48κ(L⁻¹AL⁻ᵀ)5.1‖A − LLᵀ‖/‖A‖0.0832D Laplacian, n = 100√κ ratio predicts 3.07×

    Changing the condition number on purpose

    Preconditioning is usually introduced as a trick that makes an iteration converge faster. It is not a trick. It is solving a different system with the same solution and a condition number chosen rather than inherited, and the new condition number is computable.

    rung 1 · iterative

All ladders