Accurate Eigensystem Computations by Jacobi Methods

@article{Mathias1995AccurateEC,
  title={Accurate Eigensystem Computations by Jacobi Methods},
  author={Roy Mathias},
  journal={SIAM J. Matrix Analysis Applications},
  year={1995},
  volume={16},
  pages={977-1003}
}
Demmel and Veselic showed that, subject to a minor proviso, Jacobi's method computes the eigenvalues and eigenvectors of a positive definite matrix more accurately than methods that first tridiagonalize the matrix. We extend their analysis and thereby: \begin{remunerate} \item We remove the minor proviso in their results and thus guarantee the accuracy of Jacobi's method. \item We show how to cheaply check, a posteriori, whether tridiagonalizing a particular matrix has caused a large relative… CONTINUE READING

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