Perron root bounds

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

Currently supports the bounds provided by:

• A. Melman: https://doi.org/10.1080/03081087.2012.667096
• F. Babouklis, M. Adam, N. Assimakis: DOI:10.1109/MACISE49704.2020.00016
• H. Lindqvist: https://doi.org/10.1016/S0024-3795(02)00314-2
• R. Bapat: https://doi-org.ezproxy.lib.umb.edu/2323199

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?