Normwise Scaling of Second Order Polynomial Matrices

@article{Fan2004NormwiseSO,
  title={Normwise Scaling of Second Order Polynomial Matrices},
  author={Hung-Yuan Fan and Wen-Wei Lin and Paul Van Dooren},
  journal={SIAM J. Matrix Analysis Applications},
  year={2004},
  volume={26},
  pages={252-256}
}
We propose a minimax scaling procedure for second order polynomial matrices that aims to minimize the backward errors incurred in solving a particular linearized generalized eigenvalue problem. We give numerical examples to illustrate that it can significantly improve the backward errors of the computed eigenvalue-eigenvector pairs.