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ETNA - Electronic Transactions on Numerical Analysis
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Verlag der Österreichischen Akademie der Wissenschaften Austrian Academy of Sciences Press
A-1011 Wien, Dr. Ignaz Seipel-Platz 2
Tel. +43-1-515 81/DW 3420, Fax +43-1-515 81/DW 3400 https://verlag.oeaw.ac.at, e-mail: verlag@oeaw.ac.at |
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DATUM, UNTERSCHRIFT / DATE, SIGNATURE
BANK AUSTRIA CREDITANSTALT, WIEN (IBAN AT04 1100 0006 2280 0100, BIC BKAUATWW), DEUTSCHE BANK MÜNCHEN (IBAN DE16 7007 0024 0238 8270 00, BIC DEUTDEDBMUC)
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ETNA - Electronic Transactions on Numerical Analysis, pp. 151-168, 2019/06/24
A structured backward error analysis for an approximate eigenpair of structured nonlinear matrix equations with T-palindromic, H-palindromic, T-anti-palindromic, and H-anti-palindromic structures is conducted. We construct a minimal structured perturbation in the Frobenius norm such that an approximate eigenpair becomes an exact eigenpair of an appropriately perturbed nonlinear matrix equation. The present work shows that our general framework extends existing results in the literature on the perturbation theory of matrix polynomials.
Keywords: nonlinear eigenvalue problem, even and odd matrix polynomials, palindromic matrix polynomial