1. Extensions of the Eneström-Kakeya theorem for matrix polynomials
- Author
-
Melman A.
- Subjects
matrix polynomial ,positive definite ,polynomial eigenvalue ,cauchy ,eneström-kakeya ,12d10 ,30c15 ,65h05 ,Mathematics ,QA1-939 - Abstract
The classical Eneström-Kakeya theorem establishes explicit upper and lower bounds on the zeros of a polynomial with positive coefficients and has been generalized for positive definite matrix polynomials by several authors. Recently, extensions that improve the (scalar) Eneström-Kakeya theorem were obtained with a transparent and unified approach using just a few tools. Here, the same tools are used to generalize these extensions to positive definite matrix polynomials, while at the same time generalizing the tools themselves. In the process, a framework is developed that can naturally generate additional similar results.
- Published
- 2019
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