Numerical Linear Algebra
where the algebra stops being the arithmetic
Ladder

Reduced stability — 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. 10⁻¹110¹10²-45-35-25-15-551525s, the smallest of the three interpolation pointsrightmost pole of the reduced modelunstable above this linebalanced truncation, order 3exact, and unusablefull system's pole-3.5placements swept19unstable models4worst pole24their interpolation1.3·10⁻¹⁴balanced truncation-0.84the conditions all holdand the model cannot be run

    A model that cannot be run

    A stable system, reduced by matching its transfer function at three points exactly, comes back with a pole in the right half plane at four of nineteen placements — and matches at all three points to 1.3·10⁻¹⁴ while doing it. The construction did what it promised.

    rung 1 · reduction

All ladders