Corpus ID: 235254220

Local Minimizers of the Crouzeix Ratio: A Nonsmooth Optimization Case Study

@article{Overton2021LocalMO,
  title={Local Minimizers of the Crouzeix Ratio: A Nonsmooth Optimization Case Study},
  author={M. Overton},
  journal={ArXiv},
  year={2021},
  volume={abs/2105.14176}
}
  • M. Overton
  • Published 2021
  • Computer Science, Mathematics
  • ArXiv
Given a square matrix A and a polynomial p, the Crouzeix ratio is the norm of the polynomial on the field of values of A divided by the 2-norm of the matrix p(A). Crouzeix’s conjecture states that the globally minimal value of the Crouzeix ratio is 0.5, regardless of the matrix order and polynomial degree, and it is known that 1 is a frequently occurring locally minimal value. Making use of a heavy-tailed distribution to initialize our optimization computations, we demonstrate for the first… Expand

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References

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MATH
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