The equivalence of the constrained Rayleigh quotient and Newton methods for matrix polynomials expressed in different polynomial bases along with the confluent case

DOI10.1080/00207160.2010.498509zbMath1213.65061OpenAlexW2090668213MaRDI QIDQ2995507

No author found.

Publication date: 21 April 2011

Published in: International Journal of Computer Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00207160.2010.498509

zbMATH Keywords

numerical exampleseigenvalueseigenvectorsNewton methodHermite interpolationmatrix polynomialsmatrix pencilsLU-factorizationpolynomial basesRayleigh quotient method

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Matrix pencils (15A22)

Related Items (1)

\(\lambda\)-matrix formulation applied to the Hertz contact problem with finite friction

Uses Software

• Matlab
• OPQ

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the convergence of the Rayleigh quotient iteration for the computation of the characteristic roots and vectors. I, II
• A generalized Rayleigh quotient iteration for lambda-matrices
• Block \(\mathbf {LU}\) factors of generalized companion matrix pencils
• Pseudozeros of polynomials and pseudospectra of companion matrices
• Rational approximation schemes for rotation-minimizing frames on Pythagorean-hodograph curves
• A three-stage variable-shift iteration for polynomial zeros and its relation to generalized Rayleigh iteration
• Linearization of matrix polynomials expressed in polynomial bases
• The Projected Newton Method Has Order $1 + \sqrt 2 $ for the Symmetric Eigenvalue Problem
• Spectral Methods in MATLAB
• Solving Polynomials with Small Leading Coefficients
• Barycentric Lagrange Interpolation
• The numerical stability of barycentric Lagrange interpolation
• Accuracy and Stability of Numerical Algorithms
• Symbolic computation of divided differences
• Sparse Polynomial Interpolation in Nonstandard Bases
• Iterative procedures related to relaxation methods for eigenvalue problems

This page was built for publication: The equivalence of the constrained Rayleigh quotient and Newton methods for matrix polynomials expressed in different polynomial bases along with the confluent case