Min-max elementwise backward error for roots of polynomials and a corresponding backward stable root finder
DOI10.1016/j.laa.2020.10.034zbMath1470.65094arXiv2001.05281OpenAlexW3097639912MaRDI QIDQ2029862
Marc Van Barel, Françoise Tisseur
Publication date: 4 June 2021
Published in: Linear Algebra and its Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2001.05281
zeros of polynomialstropical rootspolynomial eigenvalue problemsblock companion linearizationelementwise backward errorpolynomial root finder
Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Eigenvalues, singular values, and eigenvectors (15A18) Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) Nonlinear spectral theory, nonlinear eigenvalue problems (47J10) Matrix pencils (15A22) Numerical computation of roots of polynomial equations (65H04) Max-plus and related algebras (15A80)
Related Items (1)
Uses Software
Cites Work
- The eigenstructure of an arbitrary polynomial matrix: Computational aspects
- Backward error and condition of polynomial eigenvalue problems
- Polynomial eigenvalue solver based on tropically scaled Lagrange linearization
- Revisiting the stability of computing the roots of a quadratic polynomial
- Compatibility of approximate solution of linear equations with given error bounds for coefficients and right-hand sides
- NLEVP
- An algorithm for the complete solution of quadratic eigenvalue problems
- Tropical Scaling of Polynomial Matrices
- Accuracy and Stability of Numerical Algorithms
- Polynomial Roots from Companion Matrix Eigenvalues
- Tropical Roots as Approximations to Eigenvalues of Matrix Polynomials
- Fast and Backward Stable Computation of Roots of Polynomials
- Locating the Eigenvalues of Matrix Polynomials
This page was built for publication: Min-max elementwise backward error for roots of polynomials and a corresponding backward stable root finder
