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2017.23: Linearizations of Matrix Polynomials in Newton Bases

2017.23: Vasilije Perovic and D. Steven Mackey (2017) Linearizations of Matrix Polynomials in Newton Bases.

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Abstract

We discuss matrix polynomials expressed in a Newton basis, and the associated polynomial eigenvalue problems. Properties of the generalized ansatz spaces associated with such polynomials are proved directly by utilizing a novel representation of pencils in these spaces. Also, we show how the family of Fiedler pencils can be adapted to matrix polynomials expressed in a Newton basis. These new Newton-Fiedler pencils are shown to be strong linearizations, and some computational aspects related to them are discussed.

Item Type:MIMS Preprint
Uncontrolled Keywords:matrix polynomial, Newton bases, strong linearization, Newton-Fiedler pencil, ansatz space, updating
Subjects:MSC 2000 > 15 Linear and multilinear algebra; matrix theory
MSC 2000 > 41 Approximations and expansions
MSC 2000 > 65 Numerical analysis
MIMS number:2017.23
Deposited By:Dr. D. Steven Mackey
Deposited On:18 July 2017

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