On the Choice of Sign Defining Householder Transformations
Numerical Analysis
2023-10-10 v2 Numerical Analysis
Abstract
It is well known that, when defining Householder transformations, the correct choice of sign in the standard formula is important to avoid cancellation and hence numerical instability. In this note we point out that when the "wrong" choice of sign is used, the extent of the resulting instability depends in a somewhat subtle way on the data leading to cancellation.
Cite
@article{arxiv.2309.02443,
title = {On the Choice of Sign Defining Householder Transformations},
author = {Michael L. Overton and Pinze Yu},
journal= {arXiv preprint arXiv:2309.02443},
year = {2023}
}