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arXiv · 2508.19431

A Square-Root Free Algorithm for Computing Real Givens Rotations

Carlos F. Borges
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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.

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Carlos F. Borges. 2025-08-26. A Square-Root Free Algorithm for Computing Real Givens Rotations. https://arxiv.org/abs/2508.19431

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