Linearizations of matrix polynomials in Newton bases
Date of Original Version
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.
Linear Algebra and Its Applications
Perović, Vasilije, and D. Steven Mackey. "Linearizations of matrix polynomials in Newton bases." Linear Algebra and Its Applications 556, (2018): 1-45. doi:10.1016/j.laa.2018.06.030.