Search results for "Minimum degree algorithm"

showing 2 items of 2 documents

Size-intensive decomposition of orbital energy denominators

2000

We introduce an alternative to Almlöf and Häser’s Laplace transform decomposition of orbital energy denominators used in obtaining reduced scaling algorithms in perturbation theory based methods. The new decomposition is based on the Cholesky decomposition of positive semidefinite matrices. We show that orbital denominators have a particular short and size-intensive Cholesky decomposition. The main advantage in using the Cholesky decomposition, besides the shorter expansion, is the systematic improvement of the results without the penalties encountered in the Laplace transform decomposition when changing the number of integration points in order to control the convergence. Applications will…

Laplace transformIntegrationGeneral Physics and AstronomyMinimum degree algorithmOrbital calculations ; Perturbation theory ; Convergence of numerical methods ; Integration ; Coupled cluster calculationsPositive-definite matrixPerturbation theoryUNESCO::FÍSICA::Química físicaOrbital calculationsSpecific orbital energyPhysics and Astronomy (all)Coupled cluster calculationsComputational chemistryConvergence (routing)Decomposition (computer science)Convergence of numerical methodsApplied mathematicsPhysical and Theoretical ChemistryPerturbation theory:FÍSICA::Química física [UNESCO]Cholesky decompositionMathematics
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Method specific Cholesky decomposition : Coulomb and exchange energies

2008

We present a novel approach to the calculation of the Coulomb and exchange contributions to the total electronic energy in self consistent field and density functional theory. The numerical procedure is based on the Cholesky decomposition and involves decomposition of specific Hadamard product matrices that enter the energy expression. In this way, we determine an auxiliary basis and obtain a dramatic reduction in size as compared to the resolution of identity (RI) method. Although the auxiliary basis is determined from the energy expression, we have complete control of the errors in the gradient or Fock matrix. Another important advantage of this method specific Cholesky decomposition is t…

PhysicsPotential energy functionsBasis (linear algebra)General Physics and AstronomyMinimum degree algorithmUNESCO::FÍSICA::Química físicaPhysics and Astronomy (all)Computational chemistryFock matrixDensity functional theoryHadamard productApplied mathematicsSCF calculationsDensity functional theoryDensity functional theory ; Hadamard matrices ; Potential energy functions ; SCF calculationsHadamard matricesPhysical and Theoretical Chemistry:FÍSICA::Química física [UNESCO]ScalingCholesky decompositionSparse matrix
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