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 ISBN 978-3-7001-8258-0 Online Edition Research Article
Stefano Cipolla,
Michela Redivo-Zaglia,
Francesco Tudisco
S. 1 - 27 doi:10.1553/etna_vol53s1 Verlag der Österreichischen Akademie der Wissenschaften doi:10.1553/etna_vol53s1
Abstract: This work is concerned with the computation of $\\ell^p$-eigenvalues and eigenvectors of square tensors with $d$ modes.In the first part we propose two possible shifted variants of the popular (higher-order) power method, and, when the tensor is entry-wisenonnegative with a possibly reducible pattern and $p$ is strictly larger than the number of modes, we prove convergence of both schemes to thePerron $\\ell^p$-eigenvector and to the maximal corresponding $\\ell^p$-eigenvalue of the tensor.Then, in the second part, motivated by the slow rate of convergence that the proposed methods achieve for certain real-world tensors when$p\\approx d$, the number of modes, we introduce an extrapolation framework based on the simplified topological $\varepsilon$-algorithm to efficientlyaccelerate the shifted power sequences.Numerical results for synthetic and real world problems show the improvements gained by the introduction of the shifting parameter and the efficiency of the acceleration technique. Keywords: $\ell^p$-eigenvalues, tensors, shifted higher-order power method, extrapolation methods, Shanks transformations, ε-algorithms Published Online: 2020/01/29 08:40:43 Object Identifier: 0xc1aa5576 0x003b4192 Rights: . Electronic Transactions on Numerical Analysis (ETNA) is an electronic journal for the publication of significant new developments in numerical analysis and scientific computing. Papers of the highest quality that deal with the analysis of algorithms for the solution of continuous models and numerical linear algebra are appropriate for ETNA, as are papers of similar quality that discuss implementation and performance of such algorithms. New algorithms for current or new computer architectures are appropriate provided that they are numerically sound. However, the focus of the publication should be on the algorithm rather than on the architecture. The journal is published by the Kent State University Library in conjunction with the Institute of Computational Mathematics at Kent State University, and in cooperation with the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences (RICAM). Reviews of all ETNA papers appear in Mathematical Reviews and Zentralblatt für Mathematik. Reference information for ETNA papers also appears in the expanded Science Citation Index. ETNA is registered with the Library of Congress and has ISSN 1068-9613. …
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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 |