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Calculate bounds on the Perron (dominant) eigenvalue of nonnegative matrices

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Perron root bounds

Calculate bounds on the Perron (dominant) eigenvalue of nonnegative matrices.

Currently supports the bounds provided by:

Use cases:

To quickly estimate/bound the dominant eigenvalue can be useful in:

  • Topological entropy
  • Spectral graph theory (graph properties such as connectivity, coloring, etc.)
  • Predominant evolution of dynamical systems
  • Note: Bapat and Lindqvist are bounds of one matrix's Perron root, based on the Perron root (and corresponding eigenvectors) of another matrix

TODO:

  • Provide the example calculations from each paper
  • Find and implement other bounds
  • Catalog each bound's best use-cases
  • Ensure Bapat and Lindqvist works for zero values (only tested with positive matrices)
  • New paper by Adam et al: https://doi.org/10.1515/spma-2022-0165
    • Seems like a continued recursive strategy could be employed with "deeper" row sums?

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Calculate bounds on the Perron (dominant) eigenvalue of nonnegative matrices

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