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Mathematics > Numerical Analysis

arXiv:2211.04010 (math)
[Submitted on 8 Nov 2022]

Title:Numerical analysis of Givens rotation

Authors:Weslley da Silva Pereira, Ali Lotfi, Julien Langou
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Abstract:Generating 2-by-2 unitary matrices in floating-precision arithmetic is a delicate task. One way to reduce the accumulation error is to use less floating-point operations to compute each of the entries in the 2-by-2 unitary matrix. This paper shows an algorithm that reduces the number of operations to compute the entries of a Givens rotation. Overall, the new algorithm has more operations in total when compared to algorithms in different releases of LAPACK, but less operations per entry. Numerical tests show that the new algorithm is more accurate on average.
Subjects: Numerical Analysis (math.NA)
MSC classes: 65F30
ACM classes: G.1.3
Cite as: arXiv:2211.04010 [math.NA]
  (or arXiv:2211.04010v1 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2211.04010

Submission history

From: Weslley da Silva Pereira [view email]
[v1] Tue, 8 Nov 2022 05:04:15 UTC (730 KB)
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