A method for finding the zeros of polynomials using a companion matrix.
type: Item
instance of: scholarly article
title: A method for finding the zeros of polynomials using a companion matrix.
zbMATH Open document ID: 1040.26005
DOI: 10.1007/BF03170428
author: Xiao-Ming Niu
author: Tetsuya Sakurai
published in: Japan Journal of Industrial and Applied Mathematics
publication date: 2003-01-01T00:00:00Z
review text: In this paper the problem of finding zeros of a monic polynomial of degree \(n\) is transformed to the problem of finding eigenvalues of the corresponding companion matrix. A new method is presented by constructing a new companion matrix which has only simple eigenvalues. All the distinct zeros of a polynomial and their multiplicities can be calculated by this method.
reviewed by: Mykhaylo Pahirya
Mathematics Subject Classification ID: 26C10
Mathematics Subject Classification ID: 12D10
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 65H05
zbMATH DE Number: 2032557
zbMATH Keywords: polynomial zeros
zbMATH Keywords: companion matrix
zbMATH Keywords: multiple roots
zbMATH Keywords: eigenvalue problem
MaRDI profile type: Publication
cites work: Iteration Methods for Finding all Zeros of a Polynomial Simultaneously
cites work: Polynomial roots: The ultimate answer?
cites work: Simultaneous factorization of a polynomial by rational approximation
cites work: Construction of unitary and normal companion matrices
cites work: Expressing a polynomial as the characteristic polynomial of a symmetric matrix
cites work: Polynomial root finding using iterated Eigenvalue computation
cites work: On locating clusters of zeros of analytic functions
cites work: A fast algorithm for solving a Toeplitz system of equations
cites work: A composite polynomial zerofinding matrix algorithm
cites work: Polynomial zerofinding iterative matrix algorithms
cites work: Solving a Polynomial Equation: Some History and Recent Progress
cites work: The Triangular Decomposition of Hankel Matrices
cites work: An error analysis of two related quadrature methods for computing zeros of analytic functions.
cites work: A real symmetric tridiagonal matrix with a given characteristic polynomial
cites work: Error Bounds for Zeros of a Polynomial Based Upon Gerschgorin's Theorems
cites work: Q3857636
cites work: An Algorithm for the Inversion of Finite Hankel Matrices
cites work: Q4342463
cites work: Q4321534
full work available at URL: https://doi.org/10.1007/bf03170428
OpenAlex ID: W2061075368
description: scientific article; zbMATH DE number 2032557