Accurately Counting Singular Values of Bidiagonal Matrices and Eigenvalues of Skew-Symmetric Tridiagonal Matrices

@article{Fernando1998AccuratelyCS,
  title={Accurately Counting Singular Values of Bidiagonal Matrices and Eigenvalues of Skew-Symmetric Tridiagonal Matrices},
  author={K. Vince Fernando},
  journal={SIAM J. Matrix Analysis Applications},
  year={1998},
  volume={20},
  pages={373-399}
}
We have developed algorithms to count singular values of a real bidiagonal matrix which are greater than a specified value. This requires the transformation of the singular value problem to an equivalent symmetric eigenvalue problem. The counting of singular values is paramount in the design of bisectionand multisection-type algorithms for computing singular values on serial and parallel machines. The algorithms are based on the eigenvalues of BBt, BtB, and the 2n × 2n zero–diagonal tridiagonal… CONTINUE READING

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