Ronny Ramlau, Lothar Reichel (Hg.)

ETNA - Electronic Transactions on Numerical Analysis

 ISBN 978-3-7001-8258-0Online Edition   Research Article 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. …
 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 3402-3406, Fax +43-1-515 81/DW 3400 https://verlag.oeaw.ac.at, e-mail: verlag@oeaw.ac.at

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ETNA - Electronic Transactions on Numerical Analysis

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doi:10.1553/etna_vol47s179

doi:10.1553/etna_vol47s179

 Ronny Ramlau, Lothar Reichel (Hg.) ETNA - Electronic Transactions on Numerical Analysis ISBN 978-3-7001-8258-0Online Edition   Research Article Marilena Mitrouli, x Paraskevi Roupax  Vector estimates for f(A)b via extrapolation () S.  179 - 196doi:10.1553/etna_vol47s179doi:10.1553/etna_vol47s179 Abstract:Let $A\in\mathbb{R}^{p\times p}$ be a diagonalizable matrix and $f$ a smooth function.We are interested in the problem of approximatingthe action of $f(A)$ on a vector ${\bf b}\in\mathbb{R}^p$, i.e., $f(A){\bf b}$, without explicitlycomputing the matrix $f(A)$.In the present work, we derive families of one-term, two-term, and three-term inexpensive approximationsto the quantity $f(A){\bf b}$ via an extrapolation procedure.For a given diagonalizable matrix $A$,the proposed families of vector estimates allow us to approximate theform $W^Tf(A)U$, for any matrices $W,U\in\mathbb{R}^{p\times m}$, $1 \leq m \ll p$, not necessarily biorthogonal.We present several numerical examples to illustrate the effectivenessof our method for several functions $f$ for boththe quantity $f(A){\bf b}$ and the form $W^Tf(A)U$. Keywords:  f(A)b, vector estimates, vector moments, extrapolation, diagonalizable matricesPublished Online:  2017/11/15 13:30:45Object Identifier:  0xc1aa5576 0x00371070 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. …

 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 3402-3406, Fax +43-1-515 81/DW 3400 https://verlag.oeaw.ac.at, e-mail: verlag@oeaw.ac.at