Accurate complex Jacobi rotations
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 and , 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.
Keywords
Cite
@article{arxiv.2308.14222,
title = {Accurate complex Jacobi rotations},
author = {Vedran Novaković},
journal= {arXiv preprint arXiv:2308.14222},
year = {2024}
}
Comments
Supplementary material is available in https://github.com/venovako/AccJac and https://github.com/venovako/libpvn repositories. This is a slightly extended and enhanced version of the manuscript accepted for publication in Journal of Computational and Applied Mathematics