arxiv:2211.04010

Numerical analysis of Givens rotation

Published on Nov 8, 2022

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Abstract

An algorithm for generating 2-by-2 unitary matrices using fewer floating-point operations per entry improves numerical accuracy compared to existing algorithms in LAPACK.

AI-generated summary

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.

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