Numerical Linear Algebra
where the algebra stops being the arithmetic
Series

Least-squares — the series

One essay so far on this idea, and more questions about it than one essay answers.
  1. everything Ax can reachb = (1.1, 0.4, 1.5)Ax, the closest reachable pointr = b − Ax‖Aᵀr‖ / (‖A‖‖r‖)1.7·10⁻¹⁶‖b‖² − ‖Ax‖² − ‖r‖²1.3·10⁻¹⁵‖r‖1.3200 random nearby points of the plane were tried; none is closer.a 3×2 system, Householder QRperpendicularity is checked

    The projection and the right angle

    The least-squares solution is the one whose residual is perpendicular to everything the columns can reach. That is not a mnemonic — it is an equation, Aᵀr = 0, and the computed answer satisfies it to 10⁻¹⁶.

    part 1 · leastsquares

All series