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_vol52s249

doi:10.1553/etna_vol52s249

 Ronny Ramlau, Lothar Reichel (Hg.) ETNA - Electronic Transactions on Numerical Analysis ISBN 978-3-7001-8258-0Online Edition   Research Article Nadiia Derevianko, x Jürgen Prestinx  Approximation of Gaussians by spherical Gauss-Laguerre basis in the weighted Hilbert space () S.  249 - 269doi:10.1553/etna_vol52s249 Verlag der Österreichischen Akademie der Wissenschaften doi:10.1553/etna_vol52s249 Abstract:This paper is devoted to the study of approximation of Gaussian functions bytheir partial Fourier sums of degree $N \in \mathbb{N}$ with respect to thespherical Gauss-Laguerre (SGL) basis in the weighted Hilbert space$L_2(\mathbb{R}^3, \omega_\lambda)$, where$\omega_\lambda(|\boldsymbol{x}|)=\exp({-|\boldsymbol{x}|^2/\lambda})$,$\lambda>0$. We investigate the behavior of the corresponding error ofapproximation with respect to the scale factor $\lambda$ and order ofexpansion $N$. As interim results we obtained formulas for the Fouriercoefficients of Gaussians with respect to SGL basis in the space$L_2(\mathbb{R}^3, \omega_\lambda)$. Possible application of obtained resultsto the docking problem are described. Keywords:  spherical harmonic, Laguerre polynomial, Gaussian, hypergeometric function, molecular dockingPublished Online:  2020/05/25 11:26:00Object Identifier:  0xc1aa5576 0x003b8836 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