Polynomial zerofinders based on Szegő polynomials

DOI10.1016/S0377-0427(00)00491-XzbMath0971.65042OpenAlexW2086939507MaRDI QIDQ5929291

Gregory S. Ammar, Lothar Reichel, William B. Gragg, Daniela Calvetti

Publication date: 25 October 2001

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0377-0427(00)00491-x

zbMATH Keywords

eigenvalue problemnumerical experimentszeros of polynomialsparallel computationcontinuation methodcompanion matrixSzegő polynomialsSzegő-Hessenberg matrix

Mathematics Subject Classification ID

Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) Numerical computation of solutions to single equations (65H05) Parallel numerical computation (65Y05) Real polynomials: location of zeros (26C10)

Related Items

Parameter estimation and signal reconstruction ⋮ On a condensed form for normal matrices under finite sequences of elementary unitary similarities ⋮ Signal recovery by discrete approximation and a Prony-like method ⋮ The restarted QR-algorithm for eigenvalue computation of structured matrices

Uses Software

• EISPACK
• GAUSSIAN
• UDC

Cites Work

• A divide and conquer method for unitary and orthogonal eigenproblems
• The QR algorithm for unitary Hessenberg matrices
• Schur parameter pencils for the solution of the unitary eigenproblem
• Matrix eigensystem routines - EISPACK guide. 2nd ed
• On the condition of algebraic equations
• Positive definite Toeplitz matrices, the Arnoldi process for isometric operators, and Gaussian quadrature on the unit circle
• An updated supplementary bibliography on roots of polynomials
• A three-stage variable-shift iteration for polynomial zeros and its relation to generalized Rayleigh iteration
• Continuation methods for the computation of zeros of Szegő polynomials
• A Machine Method for Solving Polynomial Equations
• Homotopy-Determinant Algorithm for Solving Nonsymmetric Eigenvalue Problems
• Remark on Algorithms to Find Roots of Polynomials
• Corrigendum: Algorithm 730: An implementation of a divide and conquer algorithm for the unitary eigenproblem
• An implementation of a divide and conquer algorithm for the unitary eigen problem
• Polynomial Roots from Companion Matrix Eigenvalues
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