Solving polynomial eigenvalue problems by means of the Ehrlich-Aberth method
From MaRDI portal
Publication:389577
DOI10.1016/j.laa.2013.02.024zbMath1281.65061arXiv1207.6292OpenAlexW2107005172MaRDI QIDQ389577
Vanni Noferini, Dario Andrea Bini
Publication date: 21 January 2014
Published in: Linear Algebra and its Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1207.6292
numerical experimentsmatrix polynomialpolynomial eigenvalue problemEhrlich-Aberth methodNewton correctionQZ algorithmroot-finding algorithmstructured polynomials
Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Matrices over function rings in one or more variables (15A54) Matrix exponential and similar functions of matrices (15A16)
Related Items
A block-symmetric linearization of odd degree matrix polynomials with optimal eigenvalue condition number and backward error ⋮ Linearizations of matrix polynomials in Bernstein bases ⋮ Quasiseparable Hessenberg reduction of real diagonal plus low rank matrices and applications ⋮ On a class of matrix pencils and \(\ell\)-ifications equivalent to a given matrix polynomial ⋮ A Max-Plus Approach to Incomplete Cholesky Factorization Preconditioners ⋮ Solving polynomial eigenvalue problems by means of the Ehrlich-Aberth method ⋮ Incomplete LU Preconditioner Based on Max-Plus Approximation of LU Factorization ⋮ Fast optimization of viscosities for frequency‐weighted damping of second‐order systems ⋮ Accurate polynomial root-finding methods for symmetric tridiagonal matrix eigenproblems ⋮ Efficient Ehrlich-Aberth iteration for finding intersections of interpolating polynomials and rational functions ⋮ Modifications of Newton's method for even-grade palindromic polynomials and other twined polynomials ⋮ Fast and backward stable computation of eigenvalues and eigenvectors of matrix polynomials ⋮ Numerical Instability of Resultant Methods for Multidimensional Rootfinding ⋮ On Descartes' rule of signs for matrix polynomials ⋮ Computing the common zeros of two bivariate functions via Bézout resultants ⋮ On the reduction of matrix polynomials to Hessenberg form ⋮ An Algorithm for Quadratic Eigenproblems with Low Rank Damping ⋮ Matrix Polynomials with Completely Prescribed Eigenstructure ⋮ Tropical Roots as Approximations to Eigenvalues of Matrix Polynomials
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Solving polynomial eigenvalue problems by means of the Ehrlich-Aberth method
- Numerical computation of polynomial zeros by means of Aberth's method
- Modifications of Newton's method for even-grade palindromic polynomials and other twined polynomials
- Numerical methods for roots of polynomials. Part I
- Point estimation of root finding methods
- On condition numbers of polynomial eigenvalue problems
- A symplectic method for approximating all the eigenvalues of a Hamiltonian matrix
- Initial approximations in Durand-Kerner's root finding method
- An iteration formula for the simultaneous determination of the zeros of a polynomial
- Hamiltonian square roots of skew-Hamiltonian matrices
- Design, analysis, and implementation of a multiprecision polynomial rootfinder
- Polynomial eigenvalue problems with Hamiltonian structure
- On roots of functional lambda matrices
- The Ehrlich-Aberth method for palindromic matrix polynomials represented in the Dickson basis
- Backward error and condition of polynomial eigenvalue problems
- A posteriori error bounds for the zeros of polynomials
- Canonical forms for symmetric/skew-symmetric real matrix pairs under strict equivalence and congruence
- Zur iterativen Auflösung algebraischer Gleichungen
- Structure-Preserving Methods for Computing Eigenpairs of Large Sparse Skew-Hamiltonian/Hamiltonian Pencils
- The Quadratic Eigenvalue Problem
- Numerical methods for palindromic eigenvalue problems: Computing the anti-triangular Schur form
- Smith forms of palindromic matrix polynomials
- The behavior of the complete eigenstructure of a polynomial matrix under a generic rational transformation
- NLEVP
- An algorithm for the complete solution of quadratic eigenvalue problems
- On Kublanovskaya’s Approach to the Solution of the Generalized Latent Value Problem for Functional $\lambda $-Matrices
- Partition Polynomials: Asymptotics and Zeros
- Generalized Rouche's theorem and its application to multivariate autoregressions
- Condensed Forms for Skew-Hamiltonian/Hamiltonian Pencils
- Iteration Methods for Finding all Zeros of a Polynomial Simultaneously
- The Ehrlich--Aberth Method for the Nonsymmetric Tridiagonal Eigenvalue Problem
- Locating the Eigenvalues of Matrix Polynomials
- Vector Spaces of Linearizations for Matrix Polynomials
- The Conditioning of Linearizations of Matrix Polynomials
- Structured Polynomial Eigenvalue Problems: Good Vibrations from Good Linearizations
- Numerical Methods for the Tridiagonal Hyperbolic Quadratic Eigenvalue Problem
- Canonical structures for palindromic matrix polynomials
- A modified Newton method for polynomials
- Error Bounds for Zeros of a Polynomial Based Upon Gerschgorin's Theorems
- On an Approach to the Solution of the Generalized Latent Value Problem for $\lambda $-Matrices
- The Factorization of Matricial Spectral Densities
- Algorithms for the Nonlinear Eigenvalue Problem
