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Math. Softw."],"published-print":{"date-parts":[[2013,4]]},"abstract":"<jats:p>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. 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A note on weak and strong linearizations of regular matrix polynomials. Numerical analysis rep. 470 Manchester Centre for Computational Mathematics Manchester UK."},{"key":"e_1_2_1_21_1","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479804440931"},{"key":"e_1_2_1_22_1","doi-asserted-by":"crossref","unstructured":"Mackey D. S. Mackey N. Mehl C. and Mehrmann V. 2006a. Structured polynomial eigenvalue problems: Good vibrations from good linearizations. MIMS EPrint 2006.38 The University of Manchester UK. Mackey D. S. Mackey N. Mehl C. and Mehrmann V. 2006a. Structured polynomial eigenvalue problems: Good vibrations from good linearizations. 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