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One of the primary factors is found to be the norm of the block vector of coefficients of the polynomial, which is consistent with the current literature. We derive upper bounds for the backward errors for specific linearizations, and these are shown to be reasonable estimates for the computed backward errors.<\/jats:p>","DOI":"10.1137\/15m1015777","type":"journal-article","created":{"date-parts":[[2016,2,4]],"date-time":"2016-02-04T11:43:28Z","timestamp":1454586208000},"page":"123-144","source":"Crossref","is-referenced-by-count":12,"title":["Backward Error Analysis of Polynomial Eigenvalue Problems Solved by Linearization"],"prefix":"10.1137","volume":"37","author":[{"given":"Piers W.","family":"Lawrence","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Marc","family":"Van Barel","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Paul","family":"Van Dooren","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2016,2,4]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1093\/imanum\/drm051"},{"key":"atypb2","doi-asserted-by":"crossref","unstructured":"E. 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Kailath,\n Linear Systems\n , Prentice-Hall, Englewood Cliffs, NJ, 1980."},{"key":"atypb16","first-page":"72","author":"Lancaster P.","year":"2006","journal-title":"MIMS EPrint"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.13001\/1081-3810.1246"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1007\/s11075-013-9770-3"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1137\/140979034"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1016\/0898-1221(94)00202-V"},{"key":"atypb21","unstructured":"Y. Nakatsukasa and V. Noferini,\n On the stability of computing polynomial roots via confederate linearizations\n , Math. Comp. 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