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{Deur}}, \bibinfo {author} {\bibfnamefont {L.}~\bibnamefont {Mazouin}}, \
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and\ \bibinfo {author} {\bibfnamefont {E.}~\bibnamefont {Fromager}},\ }\href
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{\doibase 10.1103/PhysRevB.95.035120} {\bibfield {journal} {\bibinfo
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{journal} {Phys. Rev. B}\ }\textbf {\bibinfo {volume} {95}} (\bibinfo {year}
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{2017}),\ 10.1103/PhysRevB.95.035120}\BibitemShut {NoStop}%
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{journal} {Phys. Rev. B}\ }\textbf {\bibinfo {volume} {95}},\ \bibinfo
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{pages} {95.035120} (\bibinfo {year} {2017})}\BibitemShut {NoStop}%
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\bibitem [{\citenamefont {Deur}\ \emph {et~al.}(2018)\citenamefont {Deur},
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\citenamefont {Mazouin}, \citenamefont {Senjean},\ and\ \citenamefont
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{Fromager}}]{Deur_2018}%
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@ -1487,8 +1487,8 @@
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\bibinfo {author} {\bibfnamefont {B.}~\bibnamefont {Senjean}}, \ and\
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\bibinfo {author} {\bibfnamefont {E.}~\bibnamefont {Fromager}},\ }\href
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{\doibase 10.1140/epjb/e2018-90124-7} {\bibfield {journal} {\bibinfo
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{journal} {Eur. Phys. J. B}\ }\textbf {\bibinfo {volume} {91}} (\bibinfo
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{year} {2018}),\ 10.1140/epjb/e2018-90124-7}\BibitemShut {NoStop}%
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{journal} {Eur. Phys. J. B}\ }\textbf {\bibinfo {volume} {91}},\ \bibinfo
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{pages} {162} (\bibinfo {year} {2018})}\BibitemShut {NoStop}%
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\bibitem [{\citenamefont {Senjean}\ and\ \citenamefont
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{Fromager}(2018)}]{Senjean_2018}%
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\BibitemOpen
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%% This BibTeX bibliography file was created using BibDesk.
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%% http://bibdesk.sourceforge.net/
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%% Created for Pierre-Francois Loos at 2020-12-02 20:06:08 +0100
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%% Created for Pierre-Francois Loos at 2020-12-02 21:47:07 +0100
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%% Saved with string encoding Unicode (UTF-8)
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@ -12,9 +12,9 @@
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abstract = {This paper discusses a family of non-linear sequence-to-sequence transformations designated as ek, ekm, {\~e}k, and ed. A brief history of the transforms is related and a simple motivation for the transforms is given. Examples are given of the application of these transformations to divergent and slowly convergent sequences. In particular the examples include numerical series, the power series of rational and meromorphic functions, and a wide variety of sequences drawn from continued fractions, integral equations, geometry, fluid mechanics, and number theory. Theorems are proven which show the effectiveness of the transformations both in accelerating the convergence of (some) slowly convergent sequences and in inducing convergence in (some) divergent sequences. The essential unity of these two motives is stressed. Theorems are proven which show that these transforms often duplicate the results of well-known, but specialized techniques. These special algorithms include Newton's iterative process, Gauss's numerical integration, an identity of Euler, the Pad{\'e} Table, and Thiele's reciprocal differences. Difficulties which sometimes arise in the use of these transforms such as irregularity, non-uniform convergence to the wrong answer, and the ambiguity of multivalued functions are investigated. The concepts of antilimit and of the spectra of sequences are introduced and discussed. The contrast between discrete and continuous spectra and the consequent contrasting response of the corresponding sequences to the e1 transformation is indicated. The characteristic behaviour of a semiconvergent (asymptotic) sequence is elucidated by an analysis of its spectrum into convergent components of large amplitude and divergent components of small amplitude.},
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author = {Shanks, Daniel},
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date-added = {2020-12-02 20:05:53 +0100},
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date-modified = {2020-12-02 20:06:02 +0100},
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date-modified = {2020-12-02 21:46:29 +0100},
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doi = {https://doi.org/10.1002/sapm19553411},
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journal = {Journal of Mathematics and Physics},
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journal = {J. Math. Phys.},
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number = {1-4},
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pages = {1-42},
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title = {Non-linear Transformations of Divergent and Slowly Convergent Sequences},
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@ -89,9 +89,10 @@
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abstract = {Gross\textendash{}Oliveira\textendash{}Kohn density-functional theory (GOK-DFT) is an extension of DFT to excited states where the basic variable is the ensemble density, i.e. the weighted sum of ground- and excitedstate densities. The ensemble energy (i.e. the weighted sum of ground- and excited-state energies) can be obtained variationally as a functional of the ensemble density. Like in DFT, the key ingredient to model in GOK-DFT is the exchange-correlation functional. Developing density-functional approximations (DFAs) for ensembles is a complicated task as both density and weight dependencies should in principle be reproduced. In a recent paper [Phys. Rev. B 95, 035120 (2017)], the authors applied exact GOK-DFT to the simple but nontrivial Hubbard dimer in order to investigate (numerically) the importance of weight dependence in the calculation of excitation energies. In this work, we derive analytical DFAs for various density and correlation regimes by means of a Legendre\textendash{}Fenchel transform formalism. Both functional and density driven errors are evaluated for each DFA. Interestingly, when the ensemble exact-exchange-only functional is used, these errors can be large, in particular if the dimer is symmetric, but they cancel each other so that the excitation energies obtained by linear interpolation are always accurate, even in the strongly correlated regime.},
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author = {Deur, Killian and Mazouin, Laurent and Senjean, Bruno and Fromager, Emmanuel},
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date-added = {2020-12-02 15:57:26 +0100},
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date-modified = {2020-12-02 15:57:38 +0100},
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date-modified = {2020-12-02 21:43:28 +0100},
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doi = {10.1140/epjb/e2018-90124-7},
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journal = {Eur. Phys. J. B},
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pages = {162},
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title = {Exploring Weight-Dependent Density-Functional Approximations for Ensembles in the {{Hubbard}} Dimer},
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volume = {91},
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year = {2018},
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@ -112,9 +113,10 @@
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@article{Deur_2017,
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author = {Deur, Killian and Mazouin, Laurent and Fromager, Emmanuel},
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date-added = {2020-12-02 15:56:14 +0100},
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date-modified = {2020-12-02 15:56:22 +0100},
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date-modified = {2020-12-02 21:42:49 +0100},
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doi = {10.1103/PhysRevB.95.035120},
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journal = {Phys. Rev. B},
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pages = {95.035120},
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title = {Exact Ensemble Density Functional Theory for Excited States in a Model System: {{Investigating}} the Weight Dependence of the Correlation Energy},
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volume = {95},
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year = {2017},
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@ -157,8 +157,8 @@ Finally, we discuss several resummation techniques (such as Pad\'e and quadratic
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\maketitle
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\raggedbottom
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\tableofcontents
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%\raggedbottom
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%\tableofcontents
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%%%%%%%%%%%%%%%%%%%%%%%
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\section{Introduction}
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