Numerical Linear Algebra
where the algebra stops being the arithmetic
Ladder

Fitting — 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. 10⁻⁴10⁻³10⁻²10⁻¹110¹10²10³10⁻¹⁶10⁻¹³10⁻¹⁰10⁻⁷10⁻⁴10⁻¹relative change in the coefficients, along the worst directionrelative increase in the residualcoefficients doubled39% change, fit unmoved in the sixth digit308×: the third digit movesκ(A) = 3.6·10⁶. Exact arithmetic would pick one point on this floor. It would not raise it.24 points, degree 9, monomial basisthe data leaves them free

    The valley with no bottom

    A degree-nine fit's coefficients can be moved by a third of their own size before the residual changes in the sixth significant figure. The arithmetic did not lose those digits. The data never contained them.

    rung 3 · leastsquares

All ladders