Implicit application of polynomial filters in a k-step Arnoldi method
SIAM Journal on Matrix Analysis and Applications
On Eigenvalues of Quadratic Matrix Polynomials and Their Perturbations
SIAM Journal on Matrix Analysis and Applications
Deflation Techniques for an Implicitly Restarted Arnoldi Iteration
SIAM Journal on Matrix Analysis and Applications
Matrix computations (3rd ed.)
Convexity analysis of the largest dependent eigenvalue functions of eigensystems
Applied Mathematics and Computation
The Quadratic Eigenvalue Problem
SIAM Review
SOAR: A Second-order Arnoldi Method for the Solution of the Quadratic Eigenvalue Problem
SIAM Journal on Matrix Analysis and Applications
A monotonicity analysis theory for the dependent eigenvalues of the vibrating systems
Mathematical and Computer Modelling: An International Journal
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The main objective of this paper is to introduce an algorithm for solving dependent eigenproblems. The global matrices of these eigenproblems are formulated by using a mixed finite element approach. This approach uses both the polynomial and frequency dependent displacement fields. The algorithm that is introduced is based on solving a sequence of linear eigenproblems by an appropriate eigensolver and updating the parameter by a safeguarded zerofinder. The eigensolution technique that has been developed is designed to evaluate a specific set of parameterized eigenvalues. Numerical experiments show that this eigentechnique accurately evaluates the first ten eigenvalues of quadratic eigenproblems.