Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6416022 | Linear Algebra and its Applications | 2016 | 14 Pages |
Abstract
We first generalize to complex matrix polynomials an improvement of an upper bound by Cauchy on the zeros of complex scalar polynomials. The bound requires the unique positive root of a real scalar polynomial of the same degree as the given complex scalar or matrix polynomial. We then create a recursive procedure to represent a matrix polynomial by another matrix polynomial of larger size, but of lower degree. We apply this procedure to scalar polynomials, and then apply the generalized improved Cauchy bound to their matrix polynomial representation, often obtaining a better bound by solving a real scalar polynomial equation of significantly reduced degree.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
A. Melman,