Solving the quadratic eigenvalue problem expressed in non-monomial bases by the tropical scaling

DOI10.1007/S10444-024-10214-8MaRDI QIDQ6660071

Hongjia Chen, Xiang Wang, Chun-Hua Zhang, Teng Wang

Publication date: 10 January 2025

Published in: Advances in Computational Mathematics (Search for Journal in Brave)

zbMATH Keywords

quadratic eigenvalue problembackward errorLagrange basisNewton basisTaylor basistropical scalingblock Kronecker linearization

Mathematics Subject Classification ID

Numerical solution of nonlinear eigenvalue and eigenvector problems (65H17)

Cites Work

• A framework for analyzing nonlinear eigenproblems and parametrized linear systems
• Block Kronecker linearizations of matrix polynomials and their backward errors
• A block-symmetric linearization of odd degree matrix polynomials with optimal eigenvalue condition number and backward error
• Backward error and condition of polynomial eigenvalue problems
• On the backward error incurred by the compact rational Krylov linearization
• Polynomial eigenvalue solver based on tropically scaled Lagrange linearization
• A Backward Stable Algorithm for Quadratic Eigenvalue Problems
• Fiedler Companion Linearizations and the Recovery of Minimal Indices
• NLEVP
• Backward Error of Polynomial Eigenvalue Problems Solved by Linearization of Lagrange Interpolants
• Tropical Scaling of Polynomial Matrices
• Backward Error of Polynomial Eigenproblems Solved by Linearization
• Linearization of matrix polynomials expressed in polynomial bases
• Structured Backward Error and Condition of Generalized Eigenvalue Problems
• Normwise Scaling of Second Order Polynomial Matrices
• Conditioning and backward errors of eigenvalues of homogeneous matrix polynomials under Möbius transformations
• Backward error and conditioning of Fiedler companion linearizations
• Linearization of Lagrange and Hermite interpolating matrix polynomials
• Tropical Roots as Approximations to Eigenvalues of Matrix Polynomials
• Compact Rational Krylov Methods for Nonlinear Eigenvalue Problems
• Eigenvectors and minimal bases for some families of Fiedler-like linearizations
• The Conditioning of Linearizations of Matrix Polynomials
• Structured Polynomial Eigenvalue Problems: Good Vibrations from Good Linearizations

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