A Square-Root Free Algorithm for Computing Real Givens Rotations
Numerical Analysis
2025-08-28 v1 Numerical Analysis
Abstract
We develop an accurate square-root-free algorithm for constructing real Givens rotations. On processors that support the fused multiply-add operation in hardware, the algorithm is competitive with square-root based algorithms using a hardware square-root. Unlike the square-root-free algorithms in \cite{Hsieh1993,GENTLEMAN1973,Barlow1987,Hammarling1974ANO,Ling1989EfficientLL,Hanson,Hanson2}, our approach will construct the Givens rotation directly and is therefore applicable to a much wider variety of algorithms that use Givens rotations. We investigate the accuracy of the algorithm by simulation.
Keywords
Cite
@article{arxiv.2508.19431,
title = {A Square-Root Free Algorithm for Computing Real Givens Rotations},
author = {Carlos F. Borges},
journal= {arXiv preprint arXiv:2508.19431},
year = {2025}
}