Backward Error of Polynomial Eigenproblems Solved by Linearization

@article{Higham2007BackwardEO,
  title={Backward Error of Polynomial Eigenproblems Solved by Linearization},
  author={Nicholas J. Higham and Ren-Cang Li and Françoise Tisseur},
  journal={SIAM J. Matrix Analysis Applications},
  year={2007},
  volume={29},
  pages={1218-1241}
}
The most widely used approach for solving the polynomial eigenvalue problem P (λ)x = (∑m i=0 λ Ai ) x = 0 in n × n matrices Ai is to linearize to produce a larger order pencil L(λ) = λX + Y , whose eigensystem is then found by any method for generalized eigenproblems. For a given polynomial P , infinitely many linearizations L exist and approximate eigenpairs of P computed via linearization can have widely varying backward errors. We show that if a certain one-sided factorization relating L to… CONTINUE READING
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