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After establishing some useful properties of this matrix function, we consider the use of both polynomial and rational Krylov subspace algorithms within two types of approximations methods, namely, randomized trace estimators and probing techniques based on graph colorings. We develop error bounds and heuristics which are employed in the implementation of the algorithms. Numerical experiments on density matrices of different types of networks illustrate the performance of the methods.<\/jats:p>","DOI":"10.1007\/s00211-023-01368-6","type":"journal-article","created":{"date-parts":[[2023,9,28]],"date-time":"2023-09-28T13:02:00Z","timestamp":1695906120000},"page":"377-414","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Computation of the von Neumann entropy of large matrices via trace estimators and rational Krylov methods"],"prefix":"10.1007","volume":"155","author":[{"given":"Michele","family":"Benzi","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Michele","family":"Rinelli","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Igor","family":"Simunec","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2023,9,28]]},"reference":[{"issue":"7","key":"1368_CR1","doi-asserted-by":"crossref","DOI":"10.1063\/1.5001340","volume":"148","author":"J Aarons","year":"2018","unstructured":"Aarons, J., Skylaris, C.K.: Electronic annealing Fermi operator expansion for DFT calculations on metallic systems. 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