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2014.29: Linearizations of Matrix Polynomials in Bernstein Bases

2014.29: D. Steven Mackey and Vasilije Perovic (2014) Linearizations of Matrix Polynomials in Bernstein Bases.

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Abstract

We discuss matrix polynomials expressed in a Bernstein basis, and the associated polynomial eigenvalue problems. Using Mobius 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.

Item Type:MIMS Preprint
Uncontrolled Keywords:matrix polynomial, Bernstein polynomials, Mobius transformation, eigenvalue, spectral symmetry, companion pencil, strong linearization, structured linearization
Subjects:MSC 2000 > 15 Linear and multilinear algebra; matrix theory
MSC 2000 > 65 Numerical analysis
MIMS number:2014.29
Deposited By:Dr. D. Steven Mackey
Deposited On:01 July 2015

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