Mathematics > Numerical Analysis
arXiv:2308.14222 (math)
[Submitted on 27 Aug 2023 (v1), last revised 11 May 2024 (this version, v3)]
Title:Accurate complex Jacobi rotations
Authors:Vedran Novaković
View a PDF of the paper titled Accurate complex Jacobi rotations, by Vedran Novakovi\'c
View PDFHTML (experimental)Abstract:This note shows how to compute, to high relative accuracy under mild assumptions, complex Jacobi rotations for diagonalization of Hermitian matrices of order two, using the correctly rounded functions $\mathtt{cr\_hypot}$ and $\mathtt{cr\_rsqrt}$, proposed for standardization in the C programming language as recommended by the IEEE-754 floating-point standard. The rounding to nearest (ties to even) and the non-stop arithmetic are assumed. The numerical examples compare the observed with theoretical bounds on the relative errors in the rotations' elements, and show that the maximal observed departure of the rotations' determinants from unity is smaller than that of the transformations computed by LAPACK.
| Comments: | Supplementary material is available inthis https URL andthis https URL repositories. This is a slightly extended and enhanced version of the manuscript accepted for publication in Journal of Computational and Applied Mathematics |
| Subjects: | Numerical Analysis (math.NA); Mathematical Software (cs.MS) |
| MSC classes: | 65F15 (Primary) 65-04, 65G50 (Secondary) |
| ACM classes: | G.1.3 |
| Cite as: | arXiv:2308.14222 [math.NA] |
| (orarXiv:2308.14222v3 [math.NA] for this version) | |
| https://doi.org/10.48550/arXiv.2308.14222 arXiv-issued DOI via DataCite | |
| Journal reference: | J. Comput. Appl. Math. 450 (2024) 116003 |
| Related DOI: | https://doi.org/10.1016/j.cam.2024.116003 DOI(s) linking to related resources |
Submission history
From: Vedran Novaković [view email][v1] Sun, 27 Aug 2023 22:46:18 UTC (136 KB)
[v2] Fri, 26 Jan 2024 22:33:54 UTC (203 KB)
[v3] Sat, 11 May 2024 17:17:00 UTC (203 KB)
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View a PDF of the paper titled Accurate complex Jacobi rotations, by Vedran Novakovi\'c
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