Linearizations of matrix polynomials in Bernstein bases
Date of Original Version
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.
Linear Algebra and Its Applications
Mackey, D. Steven, and Vasilije Perović. "Linearizations of matrix polynomials in Bernstein bases." Linear Algebra and Its Applications 501, (2016): 162-197. doi:10.1016/j.laa.2016.03.019.