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By identifying the set with its homogenization, the problem is reduced to the approximation of a closed convex cone. We introduce the notion of homogeneous <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\delta $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03b4<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-approximation of a convex set and show that it defines a meaningful concept in the sense that approximations converge to the original set if the approximation error <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\delta $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03b4<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> diminishes. Moreover, we show that a homogeneous <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\delta $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03b4<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-approximation of the polar of a convex set is immediately available from an approximation of the set itself under mild conditions. Finally, we present an algorithm for the computation of homogeneous <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\delta $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03b4<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-approximations of spectrahedral shadows and demonstrate it on examples.<\/jats:p>","DOI":"10.1007\/s10957-023-02363-5","type":"journal-article","created":{"date-parts":[[2024,1,17]],"date-time":"2024-01-17T09:02:26Z","timestamp":1705482146000},"page":"874-890","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Polyhedral Approximation of Spectrahedral Shadows via Homogenization"],"prefix":"10.1007","volume":"200","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9503-3619","authenticated-orcid":false,"given":"Daniel","family":"D\u00f6rfler","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andreas","family":"L\u00f6hne","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,1,17]]},"reference":[{"issue":"3","key":"2363_CR1","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1007\/s11228-023-00687-y","volume":"31","author":"HH Bauschke","year":"2023","unstructured":"Bauschke, H.H., Bendit, T., Wang, H.: The homogenization cone: polar cone and projection. 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