Linearizations of matrix polynomials in Newton bases

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.

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