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_vol47s197

doi:10.1553/etna_vol47s197

 Ronny Ramlau, Lothar Reichel (Hg.) ETNA - Electronic Transactions on Numerical Analysis ISBN 978-3-7001-8258-0Online Edition   Research Article Nasim Eshghi, x Lothar Reichel, x Miodrag M. Spalevićx  Enhanced matrix function approximation () S.  197 - 206doi:10.1553/etna_vol47s197doi:10.1553/etna_vol47s197 Abstract:Matrix functions of the form $f(A)v$, where $A$ is a large symmetric matrix, $f$ is afunction, and $v\\ne 0$ is a vector, are commonly approximated by first applying a few,say $n$, steps of the symmetric Lanczos process to $A$ with the initial vector $v$ in order todetermine an orthogonal section of $A$. The latter is represented by a (small)$n\\times n$ tridiagonal matrix to which $f$ is applied. This approach uses the $n$ firstLanczos vectors provided by the Lanczos process. However, $n$ steps of the Lanczosprocess yield $n+1$ Lanczos vectors. This paper discusses how the $(n+1)$stLanczos vector can be used to improve the quality of the computed approximation of$f(A)v$. Also the approximation of expressions of the form $v^Tf(A)v$ is considered. Keywords:  matrix function, symmetric Lanczos process, Gauss quadraturePublished Online:  2018/02/13 13:09:54Document Date:  2018/02/13 12:56:00Object Identifier:  0xc1aa5576 0x00375bc4 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