An iterated eigenvalue algorithm for approximating roots of univariate polynomials
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Publication:697487
DOI10.1006/jsco.2002.0526zbMath1004.65060OpenAlexW2079536609MaRDI QIDQ697487
Publication date: 17 September 2002
Published in: Journal of Symbolic Computation (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1006/jsco.2002.0526
Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) Numerical computation of solutions to single equations (65H05) Real polynomials: location of zeros (26C10)
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Cites Work
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- On condition numbers and the distance to the nearest ill-posed problem
- Matrix eigensystem routines - EISPACK guide. 2nd ed
- Convergence conditions of some methods for the simultaneous computation of polynomial zero
- A bibliography on roots of polynomials
- Pseudozeros of polynomials and pseudospectra of companion matrices
- Polynomial zerofinding iterative matrix algorithms
- Design, analysis, and implementation of a multiprecision polynomial rootfinder
- The eigenstructure of an arbitrary polynomial matrix: Computational aspects
- A composite polynomial zerofinding matrix algorithm
- A remark on simultaneous inclusions of the zeros of a polynomial by Gershgorin's theorem
- Expressing a polynomial as the characteristic polynomial of a symmetric matrix
- Polynomial root finding using iterated Eigenvalue computation
- Solving a Polynomial Equation: Some History and Recent Progress
- Polynomial Roots from Companion Matrix Eigenvalues
- Error Bounds for Zeros of a Polynomial Based Upon Gerschgorin's Theorems