Block Kronecker linearizations of matrix polynomials and their backward errors

@article{Dopico2018BlockKL,
  title={Block Kronecker linearizations of matrix polynomials and their backward errors},
  author={F. Dopico and Piers W. Lawrence and J. P{\'e}rez and P. Dooren},
  journal={Numerische Mathematik},
  year={2018},
  volume={140},
  pages={373-426}
}
We introduce a new family of strong linearizations of matrix polynomials—which we call “block Kronecker pencils”—and perform a backward stability analysis of complete polynomial eigenproblems. These problems are solved by applying any backward stable algorithm to a block Kronecker pencil, such as the staircase algorithm for singular pencils or the QZ algorithm for regular pencils. This stability analysis allows us to identify those block Kronecker pencils that yield a computed complete… Expand
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