An algorithm for the complete solution of quadratic eigenvalue problems. We develop a new algorithm for the computation of all the eigenvalues and optionally the right and left eigenvectors of dense quadratic matrix polynomials. It incorporates scaling of the problem parameters prior to the computation of eigenvalues, a choice of linearization with favorable conditioning and backward stability properties, and a preprocessing step that reveals and deflates the zero and infinite eigenvalues contributed by singular leading and trailing matrix coefficients. The algorithm is backward-stable for quadratics that are not too heavily damped. Numerical experiments show that our MATLAB implementation of the algorithm, quadeig, outperforms the MATLAB function polyeig in terms of both stability and efficiency.
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References in zbMATH (referenced in 9 articles , 1 standard article )
Showing results 1 to 9 of 9.
- Hook, James; Tisseur, Françoise: Incomplete LU preconditioner based on max-plus approximation of LU factorization (2017)
- Målqvist, Axel; Peterseim, Daniel: Generalized finite element methods for quadratic eigenvalue problems (2017)
- Akian, Marianne; Bapat, Ravindra; Gaubert, Stéphane: Non-archimedean valuations of eigenvalues of matrix polynomials (2016)
- Campos, Carmen; Roman, Jose E.: Parallel Krylov solvers for the polynomial eigenvalue problem in SLEPc (2016)
- De Terán, Fernando; Dopico, Froilán M.; van Dooren, Paul: Matrix polynomials with completely prescribed eigenstructure (2015)
- Taslaman, Leo: An algorithm for quadratic eigenproblems with low rank damping (2015)
- Brugiapaglia, Simone; Gemignani, Luca: On the simultaneous refinement of the zeros of H-palindromic polynomials (2014)
- Bini, Dario A.; Noferini, Vanni: Solving polynomial eigenvalue problems by means of the Ehrlich-Aberth method (2013)
- Hammarling, Sven; Munro, Christopher J.; Tisseur, Françoise: An algorithm for the complete solution of quadratic eigenvalue problems (2013)