Browsing by Author "Thicke, K"

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    Cubic scaling algorithms for RPA correlation using interpolative separable density fitting
    (2017-04-23) Lu, J; Thicke, K
    We present a new cubic scaling algorithm for the calculation of the RPA correlation energy. Our scheme splits up the dependence between the occupied and virtual orbitals in $\chi^0$ by use of Cauchy's integral formula. This introduces an additional integral to be carried out, for which we provide a geometrically convergent quadrature rule. Our scheme also uses the newly developed Interpolative Separable Density Fitting algorithm to further reduce the computational cost in a way analogous to that of the Resolution of Identity method.
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    Orbital minimization method with ℓ1 regularization
    (Journal of Computational Physics, 2017-05-01) Lu, J; Thicke, K
    © 2017 Elsevier Inc.We consider a modification of the orbital minimization method (OMM) energy functional which contains an ℓ1 penalty term in order to find a sparse representation of the low-lying eigenspace of self-adjoint operators. We analyze the local minima of the modified functional as well as the convergence of the modified functional to the original functional. Algorithms combining soft thresholding with gradient descent are proposed for minimizing this new functional. Numerical tests validate our approach. In addition, we also prove the unanticipated and remarkable property that every local minimum of the OMM functional without the ℓ1 term is also a global minimum.