Chebyshev rootfinding via computing eigenvalues of colleague matrices: when is it stable?

DOI10.1090/mcom/3149zbMath1361.65029OpenAlexW1533206967MaRDI QIDQ2970098

Vanni Noferini, Javier J. Pérez

Publication date: 27 March 2017

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/mcom/3149

zbMATH Keywords

rootspolynomialmatrix polynomialpolynomial eigenvalue problembackward stabilitycolleague matrixChebyshev basisArnold transversality theorem

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Numerical computation of roots of polynomial equations (65H04)

Related Items (12)

Block Kronecker linearizations of matrix polynomials and their backward errors ⋮ Structured backward errors in linearizations ⋮ Mixed forward-backward stability of the two-level orthogonal Arnoldi method for quadratic problems ⋮ Constructing Strong Linearizations of Matrix Polynomials Expressed in Chebyshev Bases ⋮ Revisiting the computation of the critical points of the Keplerian distance ⋮ A Fast Algorithm for Computing Macaulay Null Spaces of Bivariate Polynomial Systems ⋮ A Class of Quasi-Sparse Companion Pencils ⋮ A boundary integral equation approach to computing eigenvalues of the Stokes operator ⋮ Backward Error Analysis of Polynomial Eigenvalue Problems Solved by Linearization ⋮ Van Dooren's Index Sum Theorem and Rational Matrices with Prescribed Structural Data ⋮ Fiedler-comrade and Fiedler--Chebyshev pencils ⋮ Rank-Structured QR for Chebyshev Rootfinding

Uses Software

• Chebfun

Cites Work

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• THE COLLEAGUE MATRIX, A CHEBYSHEV ANALOGUE OF THE COMPANION MATRIX
• Linearization of matrix polynomials expressed in polynomial bases
• Polynomial Roots from Companion Matrix Eigenvalues
• Practical Problems Arising in the Solution of Polynomial Equations
• ON MATRICES DEPENDING ON PARAMETERS

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