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Title
Asymptotic quadratic convergence of the parallel block-Jacobi EVD algorithm with dynamic ordering for Hermitian matrices
AuthorOkša, Gabriel ; Yamamoto, Yusaku ; Bečka, Martin ; Vajteršic, Marián
Published in
BIT Numerical Mathematics, Amsterdam, 2018, Vol. 58, Issue 4, page 1099-1123
PublishedAmsterdam : Springer Netherlands, 2018
LanguageEnglish
Document typeJournal Article
Keywords (EN)Parallel block-Jacobi algorithm / Dynamic ordering / Hermitian matrix / Asymptotic quadratic convergence
ISSN1572-9125
URNurn:nbn:at:at-ubs:3-11014 Persistent Identifier (URN)
DOI10.1007/s10543-018-0711-3 
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 The work is publicly available
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Asymptotic quadratic convergence of the parallel block-Jacobi EVD algorithm with dynamic ordering for Hermitian matrices [0.67 mb]
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Abstract (English)

The proof of the asymptotic quadratic convergence is provided for the parallel two-sided block-Jacobi EVD algorithm with dynamic ordering for Hermitian matrices. The discussion covers the case of well-separated eigenvalues as well as clusters of eigenvalues. Having p processors, each parallel iteration step consists of zeroing 2p off-diagonal blocks chosen by dynamic ordering with the aim to maximize the decrease of the off-diagonal Frobenius norm. Numerical experiments illustrate and confirm the developed theory.

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CC-BY-License (4.0)Creative Commons Attribution 4.0 International License