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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
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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. 83-128, 2025/02/14
This paper provides a proof of global and quadratic convergence of the block Jacobi method for Hermitian matrices under the de Rijk pivot strategy. Also global and quadratic convergence of the element-wise Jacobi method under the same pivot strategy is proved. It is shown that sharp quadratic convergence bounds can be deduced from an estimate that is obtained in the global convergence proof. Numerical tests illustrate the behavior of the methods under the de Rijk pivot strategy.
Keywords: eigenvalue problem, block Jacobi method, de Rijk pivot strategy, global convergence, quadratic convergence