A Square-Root Free Algorithm for Computing Real Givens Rotations
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916920655085568 |
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| author | Borges, Carlos F. |
| author_facet | Borges, Carlos F. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_19431 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Square-Root Free Algorithm for Computing Real Givens Rotations Borges, Carlos F. Numerical Analysis 65F99 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. |
| title | A Square-Root Free Algorithm for Computing Real Givens Rotations |
| topic | Numerical Analysis 65F99 |
| url | https://arxiv.org/abs/2508.19431 |