General polynomial roots and their multiplicities inO(N)memory andO(N2)Time∗

DOI10.1080/03081089908818625zbMath1055.12504OpenAlexW2056924749MaRDI QIDQ3836210

Frank Uhlig

Publication date: 1999

Published in: Linear and Multilinear Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03081089908818625

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Eigenvalues, singular values, and eigenvectors (15A18) Polynomials in real and complex fields: location of zeros (algebraic theorems) (12D10)

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Cites Work

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• A case against a divide and conquer approach to the nonsymmetric eigenvalue problem
• Another look at a matrix of Mark Kac
• A Divide and Conquer method for the symmetric tridiagonal eigenproblem
• Are the coefficients of a polynomial well-conditioned functions of its roots?
• A real symmetric tridiagonal matrix with a given characteristic polynomial
• The DQR algorithm, basic theory, convergence, and conditional stability
• On the condition of algebraic equations
• Polynomial roots: The ultimate answer?
• Weyl's quadtree algorithm for the unsymmetric eigenvalue problem
• Direkte Verfahren zur Berechnung der Nullstellen von Polynomen
• Gaussian elimination is not optimal
• Expressing a polynomial as the characteristic polynomial of a symmetric matrix
• A Method for Solving Algebraic Equations Using an Automatic Computer
• Remark on Algorithms to Find Roots of Polynomials
• Solving a Polynomial Equation: Some History and Recent Progress
• Forward Stability and Transmission of Shifts in the $QR$ Algorithm
• A $QL$ Procedure for Computing the Eigenvalues of Complex Symmetric Tridiagonal Matrices
• Numerical impluimentation of a new algorithm for polynomials with multiple roots