On the conditioning for heavily damped quadratic eigenvalue problem solved by linearizations

DOI10.1007/s13160-021-00492-wzbMath1481.15006OpenAlexW3211475648MaRDI QIDQ2070162

Xiang Wang, Hongjia Chen, Zongqi Cao

Publication date: 21 January 2022

Published in: Japan Journal of Industrial and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13160-021-00492-w

zbMATH Keywords

condition numberlinearizationstropical scalingheavily damped QEP

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Eigenvalues, singular values, and eigenvectors (15A18) Matrix pencils (15A22)

Uses Software

• NLEVP

Cites Work

• Unnamed Item
• Backward error and condition of polynomial eigenvalue problems
• The Quadratic Eigenvalue Problem
• A Backward Stable Algorithm for Quadratic Eigenvalue Problems
• NLEVP
• Tropical Scaling of Polynomial Matrices
• Backward Error of Polynomial Eigenproblems Solved by Linearization
• Optimal Scaling of Generalized and Polynomial Eigenvalue Problems
• Rational Krylov: A Practical Algorithm for Large Sparse Nonsymmetric Matrix Pencils
• Normwise Scaling of Second Order Polynomial Matrices
• Backward error and conditioning of Fiedler companion linearizations
• Tropical Roots as Approximations to Eigenvalues of Matrix Polynomials
• Strongly Damped Quadratic Matrix Polynomials
• Compact Rational Krylov Methods for Nonlinear Eigenvalue Problems
• The Conditioning of Linearizations of Matrix Polynomials
• Balancing Regular Matrix Pencils
• An Algorithm for Generalized Matrix Eigenvalue Problems

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