Adhikari, Bibhas Vector space of linearizations for the quadratic two-parameter matrix polynomial. (English) Zbl 1266.65058 Linear Multilinear Algebra 61, No. 5, 603-616 (2013). Summary: Given a quadratic two-parameter matrix polynomial \(Q(\lambda\mu)\), we develop a systematic approach to generating a vector space of linear two-parameter matrix polynomials. The purpose for constructing this vector space is that potential linearizations of \(Q(\lambda\mu)\) lie in it. Then, we identify a set of linearizations and describe their constructions. Finally, we determine a class of linearizations for a quadratic two-parameter eigenvalue problem. MSC: 65F15 Numerical computation of eigenvalues and eigenvectors of matrices 15A18 Eigenvalues, singular values, and eigenvectors 15A69 Multilinear algebra, tensor calculus 15A22 Matrix pencils Keywords:matrix polynomial; two-parameter matrix polynomial; quadratic two-parameter eigenvalue problem; two-parameter eigenvalue problem; linearization PDFBibTeX XMLCite \textit{B. Adhikari}, Linear Multilinear Algebra 61, No. 5, 603--616 (2013; Zbl 1266.65058) Full Text: DOI arXiv References: [1] Atkinson FV, Multiparameter Eigenvalue Problems (1972) [2] Cox D, Using Algebraic Geometry (1998) [3] De Terán F, Electron. J. Linear Algebra 18 pp 371– (2009) [4] DOI: 10.1016/j.laa.2012.03.028 · Zbl 1259.15031 [5] DOI: 10.1137/S0895479802418318 · Zbl 1077.65036 [6] DOI: 10.1016/j.laa.2011.07.026 · Zbl 1245.65042 [7] Jarlebring , E .On critical delays for linear neutral delay systems, Proceedings of the European Control Conference, Kos, Greece, 2007 [8] Jarlebring E, Ph.D. thesis (2008) [9] DOI: 10.1016/j.cam.2008.05.004 · Zbl 1166.65040 [10] DOI: 10.1016/j.laa.2009.02.008 · Zbl 1170.65063 [11] DOI: 10.1109/TAC.1980.1102482 · Zbl 0458.93046 [12] DOI: 10.1016/S1367-5788(99)90087-1 [13] DOI: 10.1007/BF02356149 · Zbl 0930.15009 [14] DOI: 10.1007/s10958-007-0079-4 [15] DOI: 10.1007/BF02355374 · Zbl 0899.65022 [16] DOI: 10.1109/9.975510 · Zbl 1007.34078 [17] DOI: 10.1137/050628350 · Zbl 1132.65027 [18] Michiels W, Advances in Design and Control 12 (2007) [19] Muhič A, Electron. J. Linear Algebra 18 pp 420– (2009) · Zbl 1190.15011 [20] DOI: 10.1016/j.laa.2009.12.022 · Zbl 1189.65070 [21] DOI: 10.1093/imamci/15.4.331 · Zbl 0918.93046 [22] Niculescu , S-I , Fu , P and Chen , J .On the stability of linear delay-differential algebraic systems: Exact conditions via matrix pencil solutions, Proceedings of the 45th IEEE Conference on Decision and Control, San Diego, California, USA, 2006 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.