An algorithm for the complete solution of quadratic eigenvalue problems

Autor:	Christopher Munro, Françoise Tisseur, Sven Hammarling
Rok vydání:	2013
Předmět:	Matrix (mathematics) Matrix differential equation Quadratic equation Linearization Applied Mathematics Computation Mathematical analysis Quadratic eigenvalue problem Algorithm Condition number Software Eigenvalues and eigenvectors Mathematics
Zdroj:	ACM Transactions on Mathematical Software. 39:1-19
ISSN:	1557-7295 0098-3500
Popis:	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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::f262db8948516e02426264ce1be67fb6 https://doi.org/10.1145/2450153.2450156 Zobrazit plný text záznamu