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By exploiting the characterizations from Mehl et al. (SIAM J. Matrix Anal. Appl. <jats:bold>37<\/jats:bold>(4), 1625\u20131654, 2016), we focus on the estimation of two stability radii for large-scale DH systems, one with respect to non-Hermitian perturbations of <jats:italic>R<\/jats:italic> in the form <jats:italic>R<\/jats:italic> + <jats:italic>B<\/jats:italic>\u0394<jats:italic>C<\/jats:italic><jats:sup><jats:italic>H<\/jats:italic><\/jats:sup> for given matrices <jats:italic>B<\/jats:italic>, <jats:italic>C<\/jats:italic>, and another with respect to Hermitian perturbations in the form <jats:italic>R<\/jats:italic> + <jats:italic>B<\/jats:italic>\u0394<jats:italic>B<\/jats:italic><jats:sup><jats:italic>H<\/jats:italic><\/jats:sup>,\u0394 = \u0394<jats:sup><jats:italic>H<\/jats:italic><\/jats:sup>. We propose subspace frameworks for both stability radii that converge at a superlinear rate in theory. The one for the non-Hermitian stability radius benefits from the DH structure-preserving model order reduction techniques, whereas for the Hermitian stability radius we derive subspaces yielding a Hermite interpolation property between the full and projected problems. With the proposed frameworks, we are able to estimate the two stability radii accurately and efficiently for large-scale systems which include a finite-element model of an industrial disk brake.<\/jats:p>","DOI":"10.1007\/s10444-020-09763-5","type":"journal-article","created":{"date-parts":[[2020,2,6]],"date-time":"2020-02-06T13:03:37Z","timestamp":1580994217000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Approximation of stability radii for large-scale dissipative Hamiltonian systems"],"prefix":"10.1007","volume":"46","author":[{"given":"Nicat","family":"Aliyev","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5051-2870","authenticated-orcid":false,"given":"Volker","family":"Mehrmann","sequence":"additional","affiliation":[]},{"given":"Emre","family":"Mengi","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,2,6]]},"reference":[{"issue":"4","key":"9763_CR1","doi-asserted-by":"publisher","first-page":"1525","DOI":"10.1121\/1.1456514","volume":"111","author":"A Akay","year":"2002","unstructured":"Akay, A.: Acoustics of friction. 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