Error estimates for the Coupled Cluster method
Thorsten Rohwedder; Reinhold Schneider
- Volume: 47, Issue: 6, page 1553-1582
- ISSN: 0764-583X
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topRohwedder, Thorsten, and Schneider, Reinhold. "Error estimates for the Coupled Cluster method." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 47.6 (2013): 1553-1582. <http://eudml.org/doc/273091>.
@article{Rohwedder2013,
abstract = {The Coupled Cluster (CC) method is a widely used and highly successful high precision method for the solution of the stationary electronic Schrödinger equation, with its practical convergence properties being similar to that of a corresponding Galerkin (CI) scheme. This behaviour has for the discrete CC method been analyzed with respect to the discrete Galerkin solution (the “full-CI-limit”) in [Schneider, 2009]. Recently, we globalized the CC formulation to the full continuous space, giving a root equation for an infinite dimensional, nonlinear Coupled Cluster operator that is equivalent the full electronic Schrödinger equation [Rohwedder, 2011]. In this paper, we combine both approaches to prove existence and uniqueness results, quasi-optimality estimates and energy estimates for the CC method with respect to the solution of the full, original Schrödinger equation. The main property used is a local strong monotonicity result for the Coupled Cluster function, and we give two characterizations for situations in which this property holds.},
author = {Rohwedder, Thorsten, Schneider, Reinhold},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {quantum chemistry; electronic Schrödinger equation; coupled cluster method; numerical analysis; nonlinear operator equation; quasi-optimality; error estimators; Galerkin method; quasi-optimal convergence},
language = {eng},
number = {6},
pages = {1553-1582},
publisher = {EDP-Sciences},
title = {Error estimates for the Coupled Cluster method},
url = {http://eudml.org/doc/273091},
volume = {47},
year = {2013},
}
TY - JOUR
AU - Rohwedder, Thorsten
AU - Schneider, Reinhold
TI - Error estimates for the Coupled Cluster method
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2013
PB - EDP-Sciences
VL - 47
IS - 6
SP - 1553
EP - 1582
AB - The Coupled Cluster (CC) method is a widely used and highly successful high precision method for the solution of the stationary electronic Schrödinger equation, with its practical convergence properties being similar to that of a corresponding Galerkin (CI) scheme. This behaviour has for the discrete CC method been analyzed with respect to the discrete Galerkin solution (the “full-CI-limit”) in [Schneider, 2009]. Recently, we globalized the CC formulation to the full continuous space, giving a root equation for an infinite dimensional, nonlinear Coupled Cluster operator that is equivalent the full electronic Schrödinger equation [Rohwedder, 2011]. In this paper, we combine both approaches to prove existence and uniqueness results, quasi-optimality estimates and energy estimates for the CC method with respect to the solution of the full, original Schrödinger equation. The main property used is a local strong monotonicity result for the Coupled Cluster function, and we give two characterizations for situations in which this property holds.
LA - eng
KW - quantum chemistry; electronic Schrödinger equation; coupled cluster method; numerical analysis; nonlinear operator equation; quasi-optimality; error estimators; Galerkin method; quasi-optimal convergence
UR - http://eudml.org/doc/273091
ER -
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