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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 502-505 |
| Number of pages | 4 |
| Journal | Numerical Algebra, Control and Optimization |
| Volume | 15 |
| Issue number | 2 |
| DOIs | |
| State | Published - Jun 2025 |
Keywords
- cancellation
- choice of sign
- Householder transformation
- numerical stability
- QR factorization
ASJC Scopus subject areas
- Algebra and Number Theory
- Control and Optimization
- Applied Mathematics