A bibliography on roots of polynomials
Journal of Computational and Applied Mathematics
Polynomial and matrix computations (vol. 1): fundamental algorithms
Polynomial and matrix computations (vol. 1): fundamental algorithms
The singular value decomposition for polynomial systems
ISSAC '95 Proceedings of the 1995 international symposium on Symbolic and algebraic computation
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
An updated supplementary bibliography on roots of polynomials
Journal of Computational and Applied Mathematics
Multivariate polynomials, duality, and structured matrices
Journal of Complexity
Computation of approximate polynomial GCDs and an extension
Information and Computation
Structured matrices and polynomials: unified superfast algorithms
Structured matrices and polynomials: unified superfast algorithms
Univariate polynomials: nearly optimal algorithms for numerical factorization and root-finding
Journal of Symbolic Computation - Computer algebra: Selected papers from ISSAC 2001
A 2002 update of the supplementary bibliography on roots of polynomials
Journal of Computational and Applied Mathematics
Real and complex polynomial root-finding with eigen-solving and preprocessing
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
Algebraic and numerical algorithms
Algorithms and theory of computation handbook
Applications of FFT and structured matrices
Algorithms and theory of computation handbook
New progress in real and complex polynomial root-finding
Computers & Mathematics with Applications
Efficient polynomial root-refiners: A survey and new record efficiency estimates
Computers & Mathematics with Applications
Real and complex polynomial root-finding by means of eigen-solving
CASC'12 Proceedings of the 14th international conference on Computer Algebra in Scientific Computing
Root-refining for a polynomial equation
CASC'12 Proceedings of the 14th international conference on Computer Algebra in Scientific Computing
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Cardinal's matrix version of the Sebastiao e Silva polynomial root-finder rapidly approximates the roots as the eigenvalues of the associated Frobenius matrix. We preserve rapid convergence to the roots but amend the algorithm to allow input polynomials with multiple roots and root clusters. As in Cardinal's algorithm, we repeatedly square the Frobenius matrix in nearly linear arithmetic time per squaring, which yields dramatic speedup versus the recent effective polynomial root-finder based on the application of the inverse power method to the Frobenius matrix.