Estimations of zeros of a polynomial using numerical radius inequalities

2020/01/27 by Pintu Bhunia, Bhunia, Pintu, Santanu Bag +5
Computer Science · Mathematics · #15A60 #Advanced Optimization Algorithms Research #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical functions and polynomials #Matrix Theory and Algorithms #Primary 26C20 #Secondary 47A12 #math.FA #msc:15A60 #msc:26C20 #msc:47A12

paper · pdf · doi:10.48550/arxiv.2001.09706

12 pages

arxiv created 2020/01/27 · openalex publication_date 2020/01/27 · arxiv updated 2020/01/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present new bounds for the numerical radius of bounded linear operators and 2× 2 operator matrices. We apply upper bounds for the numerical radius to the Frobenius companion matrix of a complex monic polynomial to obtain new estimations for zeros of that polynomial. We also show with numerical examples that our new estimations improve on the existing estimations.

Related

• Bounding the zeros of polynomials using the Frobenius companion matrix partitioned by the Cartesian decomposition
• New lower bound for numerical radius for off-diagonal 2× 2 matrices
• New upper bounds for the q-numerical radius of Hilbert space operators
• Improvement of numerical radius inequalities
• Some improvements of numerical radius inequalities of operators and operator matrices