Polynomial roots: The ultimate answer?

DOI10.1016/0024-3795(93)00341-VzbMath0836.65070MaRDI QIDQ1899387

Luigi Brugnano, Donato Trigiante

Publication date: 9 October 1995

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

zbMATH Keywords

convergencenumerical resultseigenvaluestridiagonal matrixQR factorizationblock diagonal matrixroots of a polynomial

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) Integral representations of finite groups (20C10)

Related Items

A composite polynomial zerofinding matrix algorithm, Bounds for the zeros of polynomials from eigenvalues and singular values of some companion matrices, Computing the Jordan Structure of an Eigenvalue, Continued fractions as dynamical systems, A method for finding the zeros of polynomials using a companion matrix., Finding all real roots of a polynomial by matrix algebra and the Adomian decomposition method, Computing multiple roots of inexact polynomials, General polynomial roots and their multiplicities inO(N)memory andO(N²)Time^∗

Cites Work

• Simultaneous determination of polynomial roots and multiplicities: An algorithm and related problems
• A three-stage variable-shift iteration for polynomial zeros and its relation to generalized Rayleigh iteration
• Ein Gesamtschrittverfahren zur Berechnung der Nullstellen von Polynomen
• A Globally Convergent Method for Simultaneously Finding Polynomial Roots
• Reduction to Tridiagonal Form and Minimal Realizations
• Reduction of a General Matrix to Tridiagonal Form
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item