New progress in real and complex polynomial root-finding
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Publication:552308
DOI10.1016/j.camwa.2010.12.070zbMath1217.65087OpenAlexW2053020126MaRDI QIDQ552308
Publication date: 21 July 2011
Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.camwa.2010.12.070
eigenvalueseigenvectorssecular equationreal rootscompanion matricespolynomial root-finding\texttt{DPR1}\texttt{EIGENSOLVE}\texttt{Fortune} package\texttt{MPSOLVE}DPR1 matriceshomotopy continuation methodsRayleigh quotients
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Cites Work
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- Matrix computations and polynomial root-finding with preprocessing
- Numerical computation of polynomial zeros by means of Aberth's method
- An iterated eigenvalue algorithm for approximating roots of univariate polynomials
- Univariate polynomials: Nearly optimal algorithms for numerical factorization and root-finding
- Linear construction of companion matrices
- Additive preconditioning for matrix computations
- A fast implicit QR eigenvalue algorithm for companion matrices
- Numerical methods for roots of polynomials. Part I
- Additive preconditioning, eigenspaces, and the inverse iteration
- Randomized preprocessing of homogeneous linear systems of equations
- Rayleigh quotient algorithms for nonsymmetric matrix pencils
- New fast algorithms for polynomial interpolation and evaluation on the Chebyshev node set
- A new look at the Lanczos algorithm for solving symmetric systems of linear equations
- A probabilistic remark on algebraic program testing
- Partial fraction decomposition in \(\mathbb{C}(z)\) and simultaneous Newton iteration for factorization in \(\mathbb{C}^{[z}\)]
- Polynomial zerofinding iterative matrix algorithms
- Inverse power and Durand-Kerner iterations for univariate polynomial root-finding
- Design, analysis, and implementation of a multiprecision polynomial rootfinder
- Symbolic and numeric methods for exploiting structure in constructing resultant matrices
- Fast and stable QR eigenvalue algorithms for generalized companion matrices and secular equations
- Analysis of the quasi-Laguerre method
- Multivariate polynomials, duality, and structured matrices
- Approximating complex polynomial zeros: modified Weyl's quadtree construction and improved Newton's iteration.
- Graeffe's, Chebyshev-like, and Cardinal's processes for splitting a polynomial into factors
- Schur aggregation for linear systems and determinants
- The amended DSeSC power method for polynomial root-finding
- Root-squaring with DPR1 matrices
- Real and complex polynomial root-finding with eigen-solving and preprocessing
- Random polynomials and expected complexity of bisection methods for real solving
- The DMM bound
- A Newton-Raphson method for moving-average spectral factorization using the Euclid algorithm
- A Parallel and Vector Variant of the Cyclic Reduction Algorithm
- The Euclid algorithm and the fast computation of cross-covariance and autocovariance sequences
- Inverse Iteration, Ill-Conditioned Equations and Newton’s Method
- Fast Probabilistic Algorithms for Verification of Polynomial Identities
- Some modifications of Laguerre's method
- Polynomial Root-Finding Algorithms and Branched Covers
- Solving a Polynomial Equation: Some History and Recent Progress
- Templates for the Solution of Algebraic Eigenvalue Problems
- Solving Polynomials with Small Leading Coefficients
- Quasi-Laguerre Iteration in Solving Symmetric Tridiagonal Eigenvalue Problems
- Accuracy and Stability of Numerical Algorithms
- A Jacobi–Davidson Iteration Method for Linear Eigenvalue Problems
- Fast QR Eigenvalue Algorithms for Hessenberg Matrices Which Are Rank‐One Perturbations of Unitary Matrices
- Laguerre's Method Applied to the Matrix Eigenvalue Problem
- The Matrix Eigenvalue Problem
- Factorization of the Covariance Generating Function of a Pure Moving Average Process
- Some Modified Matrix Eigenvalue Problems
- A unifying convergence analysis of second-order methods for secular equations
- The quasi-Laguerre iteration
- Nichtlineare Behandlung von Eigenwertaufgaben
- On the geometry of Graeffe iteration
- How to find all roots of complex polynomials by Newton's method.
