Linearizations of matrix polynomials in Bernstein bases

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• 作者：D. Steven Mackey^a ; ^{steve.mackey@wmich.edu" class="auth_mail" title="E-mail the corresponding author} ; Vasilije Perović^b ; ^{perovic@uri.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：65D17 ; 65F15 ; 15A18 ; 15A21 ; 15A22 ; 41A10
• 刊名：Linear Algebra and its Applications
• 出版年：2016
• 出版时间：15 July 2016
• 年：2016
• 卷：501
• 期：Complete
• 页码：162-197
• 全文大小：667 K

文摘

We discuss matrix polynomials expressed in a Bernstein basis, and the associated polynomial eigenvalue problems. Using Möbius transformations of matrix polynomials, large new families of strong linearizations are generated. Matrix polynomials that are structured with respect to a Bernstein basis, together with their associated spectral symmetries, are also investigated. The results in this paper apply equally well to scalar polynomials, and include the development of new companion pencils for polynomials expressed in a Bernstein basis.