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A class of cubic and quintic spline modified collocation methods for the solution of two-point boundary value problems
This paper is concerned with the study of a class of methods for solving second and fourth-order two-point boundary-value problems. The methods under
consideration are modifications of the standard cubic and quintic spline
collocation techniques, and are derived by making use of recent results con- cerning the a posteriori correction of cubic and quintic interpolating spline
On the equivalence of LIST and DIIS methods for convergence acceleration
Self-consistent field extrapolation methods play a pivotal role in quantum
chemistry and electronic structure theory. We here demonstrate the mathematical
equivalence between the recently proposed family of LIST methods [J. Chem.
Phys. 134, 241103 (2011); J. Chem. Theory Comput. 7, 3045 (2011)] with Pulay's
DIIS [Chem. Phys. Lett. 73, 393 (1980)]. Our results also explain the
differences in performance among the various LIST methods
Systematic study of infrared energy corrections in truncated oscillator spaces
We study the convergence properties of nuclear binding energies and
two-neutron separation energies obtained with self-consistent mean-field
calculations based on the Hartree-Fock-Bogolyubov (HFB) method with Gogny-type
effective interactions. Owing to lack of convergence in a truncated working
basis, we employ and benchmark one of the recently proposed infrared energy
correction techniques to extrapolate our results to the limit of an infinite
model space. We also discuss its applicability to global calculations of
nuclear masses.Comment: 12 pages, 12 figure
Application of the Density Matrix Renormalization Group in momentum space
We investigate the application of the Density Matrix Renormalization Group
(DMRG) to the Hubbard model in momentum-space. We treat the one-dimensional
models with dispersion relations corresponding to nearest-neighbor hopping and
hopping and the two-dimensional model with isotropic nearest-neighbor
hopping. By comparing with the exact solutions for both one-dimensional models
and with exact diagonalization in two dimensions, we first investigate the
convergence of the ground-state energy. We find variational convergence of the
energy with the number of states kept for all models and parameter sets. In
contrast to the real-space algorithm, the accuracy becomes rapidly worse with
increasing interaction and is not significantly better at half filling. We
compare the results for different dispersion relations at fixed interaction
strength over bandwidth and find that extending the range of the hopping in one
dimension has little effect, but that changing the dimensionality from one to
two leads to lower accuracy at weak to moderate interaction strength. In the
one-dimensional models at half-filling, we also investigate the behavior of the
single-particle gap, the dispersion of spinon excitations, and the momentum
distribution function. For the single-particle gap, we find that proper
extrapolation in the number of states kept is important. For the spinon
dispersion, we find that good agreement with the exact forms can be achieved at
weak coupling if the large momentum-dependent finite-size effects are taken
into account for nearest-neighbor hopping. For the momentum distribution, we
compare with various weak-coupling and strong-coupling approximations and
discuss the importance of finite-size effects as well as the accuracy of the
DMRG.Comment: 15 pages, 11 eps figures, revtex
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