Bidiagonalization using Householder transformations

The previous post was a discussion on employing Householder transformations to perform a QR decomposition. This post will be short. I've had this code lying around for a while now and thought I would make it available. The process of bidiagonalization using Householder transformations amounts to nothing more than alternating by left and right transformations. The cMatrix::householderBidiagonalization() method: Download the source: qr_householder_bidiagonalization.cc.bz2 Read more [...]

QR decomposition using Householder transformations

It's been a while since my last post. A project I have in the works requires some matrix decompositions, so I thought this would be a good opportunity to get a post out about QR decompositions using Householder transformations. For the moment we will focus on the field of real numbers, though we can extend these concepts to the complex field if necessary. Theorem. A real matrix, , can be decomposed as , where $$\mathbf{Q} Read more [...]