An Algorithm for Quadratic Eigenproblems with Low Rank Damping

DOI10.1137/140969099zbMath1315.65039OpenAlexW2045211476MaRDI QIDQ5251735

Leo Taslaman

Publication date: 21 May 2015

Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/140969099

zbMATH Keywords

algorithmnumerical experimentsemidefinite matrixquadratic eigenvalue problemmatrix polynomialvibrating systemEhrlich-Aberth iterationeigenvalue algorithmdefinite generalized eigenvalue problemdiscrete damperlow rank damping

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Systems arising from the discretization of structural vibration problems (70J50) Free motions in linear vibration theory (70J30)

Related Items (3)

Fast optimization of viscosities for frequency‐weighted damping of second‐order systems ⋮ Numerical Instability of Resultant Methods for Multidimensional Rootfinding ⋮ Strongly Damped Quadratic Matrix Polynomials

Uses Software

• NLEVP
• quadeig

Cites Work

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• Solving polynomial eigenvalue problems by means of the Ehrlich-Aberth method
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• A Padé approximate linearization algorithm for solving the quadratic eigenvalue problem with low-rank damping
• NLEVP
• An algorithm for the complete solution of quadratic eigenvalue problems
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• Matrix Analysis
• Inverse Iteration, Ill-Conditioned Equations and Newton’s Method
• An Algorithm for $Ax = \lambda Bx$ with Symmetric and Positive-Definite A and B
• A Block Algorithm for Matrix 1-Norm Estimation, with an Application to 1-Norm Pseudospectra
• Normwise Scaling of Second Order Polynomial Matrices
• Iteration Methods for Finding all Zeros of a Polynomial Simultaneously
• Strongly Damped Quadratic Matrix Polynomials
• SOAR: A Second-order Arnoldi Method for the Solution of the Quadratic Eigenvalue Problem
• A modified Newton method for polynomials

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