APPROXIMATIONS FOR VON NEUMANN AND RENYI ENTROPIES OF GRAPHS USING THE EULER-MACLAURIN FORMULA

作者:Bebiano, Natalia*; Furtado, Susana; da Providencia, Joao; Xu, Wei-Ru; da Providencia, Joao P.
来源:Electronic Transactions on Numerical Analysis, 2018, 48: 227-242.
DOI:10.1553/etna_vol48s227

摘要

There have been many attempts of understanding graph structures by investigating graph entropies. In this article we investigate approximations for von Neumann and Renyi-alpha entropies of paths and rings, using the Euler-Maclaurin summation formula. For alpha an integer, the approximations become exact, and, in general, the obtained estimates have a remarkable degree of accuracy.

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