Stability of rootfinding for barycentric Lagrange interpolants

DOI10.1007/s11075-013-9770-3zbMath1297.65051OpenAlexW1969652671MaRDI QIDQ2454385

Piers W. Lawrence, Robert M. Corless

Publication date: 13 June 2014

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-013-9770-3

zbMATH Keywords

stabilitynumerical exampleseigenvalue problemLagrange interpolationpolynomial rootsbackward errorbarycentric formulageneralized companion matrices

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Numerical interpolation (65D05) Numerical solution of nonlinear eigenvalue and eigenvector problems (65H17) Numerical computation of roots of polynomial equations (65H04)

Related Items (11)

Block Kronecker linearizations of matrix polynomials and their backward errors ⋮ Structured backward errors in linearizations ⋮ A real QZ algorithm for structured companion pencils ⋮ Chebyshev rootfinding via computing eigenvalues of colleague matrices: when is it stable? ⋮ Algebraic linearizations of matrix polynomials ⋮ Bivariate barycentric rational interpolation method for two dimensional fractional Volterra integral equations ⋮ Numerical algorithm based on extended barycentric Lagrange interpolant for two dimensional integro-differential equations ⋮ Conversions between barycentric, RKFUN, and Newton representations of rational interpolants ⋮ The Largest Roots of the Mandelbrot Polynomials ⋮ Backward Error Analysis of Polynomial Eigenvalue Problems Solved by Linearization ⋮ On the stability of computing polynomial roots via confederate linearizations

Uses Software

• LAPACK

Cites Work

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• Die Lage der Nullstellen eines Polynoms
• THE COLLEAGUE MATRIX, A CHEBYSHEV ANALOGUE OF THE COMPANION MATRIX
• Backward Error of Polynomial Eigenproblems Solved by Linearization
• LAPACK Users' Guide
• On eigenvectors and adjoints of modified matrices
• Balancing the Generalized Eigenvalue Problem
• Barycentric Lagrange Interpolation
• The Derivative of a Determinant
• Polynomial Roots from Companion Matrix Eigenvalues
• The Matrix Eigenvalue Problem
• Balancing Regular Matrix Pencils
• Roots of Polynomials Expressed in Terms of Orthogonal Polynomials
• ON MATRICES DEPENDING ON PARAMETERS

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