{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,22]],"date-time":"2026-08-22T07:04:26Z","timestamp":1787382266948,"version":"build-2736575974"},"reference-count":35,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","funder":[{"name":"Belgian Network DYSCO"},{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["EP\/I005293"],"award-info":[{"award-number":["EP\/I005293"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Matrix Anal. Appl."],"published-print":{"date-parts":[[2017,1]]},"abstract":"<jats:p>The need to solve polynomial eigenvalue problems for matrix polynomials expressed in nonmonomial bases has become very important. Among the most important bases in numerical applications are the Chebyshev polynomials of the first and second kind. In this work, we introduce a new approach for constructing strong linearizations for matrix polynomials expressed in Chebyshev bases, generalizing the classical colleague pencil, and expanding the arena in which to look for linearizations of matrix polynomials expressed in Chebyshev bases. We show that any of these linearizations is a strong linearization regardless of whether the matrix polynomial is regular or singular. In addition, we show how to recover eigenvectors, minimal indices, and minimal bases of the polynomial from those of any of the new linearizations. As an example, we also construct strong linearizations for matrix polynomials of odd degree that are symmetric (resp., Hermitian) whenever the matrix polynomials are symmetric (resp., Hermitian).<\/jats:p>","DOI":"10.1137\/16m105839x","type":"journal-article","created":{"date-parts":[[2017,7,27]],"date-time":"2017-07-27T11:51:43Z","timestamp":1501156303000},"page":"683-709","source":"Crossref","is-referenced-by-count":9,"title":["Constructing Strong Linearizations of Matrix Polynomials Expressed in Chebyshev Bases"],"prefix":"10.1137","volume":"38","author":[{"given":"Piers W.","family":"Lawrence","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Javier","family":"P\u00e9rez","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2017,7,27]]},"reference":[{"key":"atypb1","unstructured":"M. Abramowitz and I. A. Stegun, eds.\n                      Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables\n                      , Dover Publications, Inc., New York, 1972."},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1093\/imanum\/drm051"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(94)00158-8"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1137\/0609006"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479803429788"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1137\/151004847"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2015.03.032"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(84)90203-9"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1137\/090772927"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2011.09.010"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2014.07.007"},{"key":"atypb12","first-page":"1","author":"De Ter\u00e1n F.","year":"2015","journal-title":"IMA J. Numer. Anal., ("},{"key":"atypb14","unstructured":"T. A. Driscoll, N. Hale, and L. N. Trefethen,\n                      Chebfun Guide\n                      , Pafnuty Publications, 2014,http:\/\/www.chebfun.org\/docs\/guide\/."},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1007\/s10543-012-0381-5"},{"key":"atypb16","unstructured":"D. K. Faddeev and I. S. Sominski\u012d,\n                      Problems in Higher Algebra\n                      , translated from the Russian by G. Yankovsky, Mir, Moscow, 1978."},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1137\/0313029"},{"key":"atypb18","unstructured":"I. Gohberg, P. Lancaster, and L. 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