This is a review of the Golub-Kahan Bidiagonalization Method, using Householder reflectors. The method was developed in 1965 by Gene H Golub and William M Kahan to eliminate problems from ill-conditioned or rank-deficient matrices. This method used in numerous algorithms including LSQR and SVD.
The notebook focuses on explaning the big picture overview of the Golub-Kahan method:
I include a digression on Householder reflectors and their role in bidiagonalization:
As well as an example of the algorithm:
