Fast Computation of the Zeros of a Polynomial via Factorization of the Companion Matrix
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Publication:4917134
DOI10.1137/120865392zbMath1264.65074OpenAlexW2035754171MaRDI QIDQ4917134
Jared Lee Aurentz, David S. Watkins, Raf Vandebril
Publication date: 29 April 2013
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/120865392
numerical exampleseigenvalueszeros of a polynomialerror estimateFrobenius companion matrix\(QR\) algorithm
Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Numerical computation of roots of polynomial equations (65H04)
Related Items (11)
Fast and Backward Stable Computation of Roots of Polynomials, Part II: Backward Error Analysis; Companion Matrix and Companion Pencil ⋮ Pentadiagonal companion matrices ⋮ Fast computation of eigenvalues of companion, comrade, and related matrices ⋮ Factoring Block Fiedler Companion Matrices ⋮ Inverse eigenvalue problems for extended Hessenberg and extended tridiagonal matrices ⋮ Companion matrix patterns ⋮ Bounds for the Distance to the Nearest Correlation Matrix ⋮ A CMV-Based Eigensolver for Companion Matrices ⋮ Fast and backward stable transforms between spherical harmonic expansions and bivariate Fourier series ⋮ The Polynomial Eigenvalue Problem is Well Conditioned for Random Inputs ⋮ Fast and Backward Stable Computation of Roots of Polynomials
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