Implementation of Jacobi Rotations for Accurate Singular Value Computation in Floating Point Arithmetic

@article{Drmac1997ImplementationOJ,
  title={Implementation of Jacobi Rotations for Accurate Singular Value Computation in Floating Point Arithmetic},
  author={Zlatko Drmac},
  journal={SIAM J. Scientific Computing},
  year={1997},
  volume={18},
  pages={1200-1222}
}
In this paper we con if \begin{displaymath} 1 - m\r value decomposition (SVD) $A=U\Sigma V^{\tau}$ of $A=[a_1,a_2]\in\R^{m\times 2}$ accurately in floating point arithmetic. It is shown how the rotation angacobi rotation $V$ (the right singular vector matrix) and how to compute $AV=U\Sigma$ even if the floating point representation of $V$ is the identity matrix. In the case $\ns{a_1}\gg\ns{a_2}$, underflow can produce the identity matrix as the floating point value of $V$, even for $a_1$, $a_2… CONTINUE READING

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