Polynomial eigenvalue solver based on tropically scaled Lagrange linearization

DOI10.1016/j.laa.2017.04.025zbMath1418.65052OpenAlexW2584009765MaRDI QIDQ2002779

Françoise Tisseur, Marc Van Barel

Publication date: 12 July 2019

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

Full work available at URL: https://www.research.manchester.ac.uk/portal/en/publications/polynomial-eigenvalue-solver-based-on-tropically-scaled-lagrange-linearization(2d15f7a3-a8e0-4bf0-98ac-7316d0468071).html

zbMATH Keywords

linearizationpolynomial eigenvalue problemblock companion linearizationLagrange-type linearizationtropical scalingwell-separated tropical roots

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Eigenvalues, singular values, and eigenvectors (15A18) Nonlinear spectral theory, nonlinear eigenvalue problems (47J10) Matrix pencils (15A22) Max-plus and related algebras (15A80)

Related Items (7)

A block-symmetric linearization of odd degree matrix polynomials with optimal eigenvalue condition number and backward error ⋮ An Algorithm for the Complete Solution of the Quartic Eigenvalue Problem ⋮ Incomplete LU Preconditioner Based on Max-Plus Approximation of LU Factorization ⋮ A comparison of eigenvalue condition numbers for matrix polynomials ⋮ Factoring Block Fiedler Companion Matrices ⋮ Min-max elementwise backward error for roots of polynomials and a corresponding backward stable root finder ⋮ Conditioning and backward errors of eigenvalues of homogeneous matrix polynomials under Möbius transformations

Uses Software

• NLEVP
• advanpix
• quadeig

Cites Work

• Backward error and condition of polynomial eigenvalue problems
• Backward Error Analysis of Polynomial Eigenvalue Problems Solved by Linearization
• Polynomial Eigenvalue Problems: Theory, Computation, and Structure
• NLEVP
• An algorithm for the complete solution of quadratic eigenvalue problems
• Tropical Scaling of Polynomial Matrices
• Backward Error of Polynomial Eigenproblems Solved by Linearization
• Linearization of matrix polynomials expressed in polynomial bases
• Scaling, sensitivity and stability in the numerical solution of quadratic eigenvalue problems
• Structured Backward Error and Condition of Generalized Eigenvalue Problems
• Linearization of Lagrange and Hermite interpolating matrix polynomials
• Tropical Roots as Approximations to Eigenvalues of Matrix Polynomials
• Fast and Backward Stable Computation of Roots of Polynomials
• Locating the Eigenvalues of Matrix Polynomials
• The Conditioning of Linearizations of Matrix Polynomials

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