Improved initialization of the accelerated and robust QR-like polynomial root-finding

zbMath1065.65065MaRDI QIDQ1772043

Luca Gemignani, Pan, Victor Y., Dario Andrea Bini

Publication date: 15 April 2005

Published in: ETNA. Electronic Transactions on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/124809

zbMATH Keywords

numerical examplesMöbius transformationpolynomial rootssemiseparable matricesQR iterationeigenvalue computation

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) 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) Real polynomials: location of zeros (26C10)

Related Items

The amended DSeSC power method for polynomial root-finding, Additive preconditioning and aggregation in matrix computations, Efficient polynomial root-refiners: a survey and new record efficiency estimates, Root-squaring with DPR1 matrices, Neville elimination for rank-structured matrices, Eigen-solving via reduction to DPR1 matrices, Linking the TPR1, DPR1 and arrow-head matrix structures, Additive preconditioning, eigenspaces, and the inverse iteration, Generalizations of Gershgorin disks and polynomial zeros, Solving secular and polynomial equations: a multiprecision algorithm, Fast and stable QR eigenvalue algorithms for generalized companion matrices and secular equations, A unitary Hessenberg \(QR\)-based algorithm via semiseparable matrices, The polynomial pivots as initial values for a new root-finding iterative method, Coefficient-free adaptations of polynomial root-finders

Uses Software

• JDQR
• JDQZ