On computing givens rotations reliably and efficiently

@article{Bindel2002OnCG,
  title={On computing givens rotations reliably and efficiently},
  author={David Bindel and James Demmel and William Kahan and Osni Marques},
  journal={ACM Trans. Math. Softw.},
  year={2002},
  volume={28},
  pages={206-238}
}
We consider the efficient and accurate computation of Givens rotations. When <i>f</i> and <i>g</i> are positive real numbers, this simply amounts to computing the values of <i>c</i> = <i>f</i>/√<i>f</i><sup>2</sup> + <i>g</i><sup>2</sup>, <i>s</i> = <i>g</i>/√<i>f</i><sup>2</sup> + <i>g</i><sup>2</sup>, and <i>r</i> = √<i>f</i><sup>2</sup> + <i>g</i><sup>2</sup>. This apparently trivial computation merits closer consideration for the following three reasons. First, while the definitions of <i>c… CONTINUE READING
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