Related papers: $SO(3)$ quadratures in angular-momentum projection
Molecular line lists, particularly those computed for high temperature applications, often have very few states assigned local quantum numbers. These are often important components for accurately determining line shape parameters required…
The ongoing progress in (nuclear) many-body theory is accompanied by an ever-rising increase in complexity of the underlying formalisms used to solve the stationary Schr\"odinger equation. The associated working equations at play in…
We have recently developed an efficient method of performing the full quantum number projection from the most general mean-field (HFB type) wave functions including the angular momentum, parity as well as the proton and neutron particle…
This paper presents a high-order accurate numerical quadrature algorithm for evaluating integrals over curved surfaces and regions defined implicitly via a level set of a given function restricted to a hyperrectangle. The domain is divided…
We propose general non-accelerated and accelerated tensor methods under inexact information on the derivatives of the objective, analyze their convergence rate. Further, we provide conditions for the inexactness in each derivative that is…
Random projection can reduce the dimension of data while capturing its structure and is a fundamental tool for machine learning, signal processing, and information retrieval, which deal with a large amount of data today. RandNLA (Randomized…
This paper reports investigations on the computation of material fronts in multi-fluid models using a Lagrange-Projection approach. Various forms of the Projection step are considered. Particular attention is paid to minimization of…
Kernel quadratures and other kernel-based approximation methods typically suffer from prohibitive cubic time and quadratic space complexity in the number of function evaluations. The problem arises because a system of linear equations needs…
We introduce a novel representation and optimization framework for discrete geodesics on triangle meshes that reduces artifacts of linear methods on uneven and coarse discretizations. Our method computes squared geodesic distances from…
We study the properties of the nuclear rotational excitations with hypothetical tetrahedral symmetry by employing the microscopic mean-field and residual-interaction Hamiltonians with angular-momentum and parity projection method; we focus…
The optical properties of nanoparticles can be substantially affected by their assembly in compact aggregates. This is a common situation notably for nanoparticles synthesised and self-assembled into rigid clusters in colloidal form, where…
Designing efficient quasi-Newton methods is an important problem in nonlinear optimization and the solution of systems of nonlinear equations. From the perspective of the matrix approximation process, this paper presents a unified framework…
Statistical learning methods show great promise in providing an accurate prediction of materials and molecular properties, while minimizing the need for computationally demanding electronic structure calculations. The accuracy and…
In this article we propose a new adaptive numerical quadrature procedure which includes both local subdivision of the integration domain, as well as local variation of the number of quadrature points employed on each subinterval. In this…
We describe how to approximate the Riemann curvature tensor as well as sectional curvatures on possibly infinite-dimensional shape spaces that can be thought of as Riemannian manifolds. To this end, we extend the variational time…
When modeling physical properties of molecules with machine learning, it is desirable to incorporate $SO(3)$-covariance. While such models based on low body order features are not complete, we formulate and prove general completeness…
We propose a new modified primal-dual proximal best approximation method for solving convex not necessarily differentiable optimization problems. The novelty of the method relies on introducing memory by taking into account iterates…
We investigate quadrature rules for measures supported on real algebraic and rational curves, focusing on the {odd-degree} case \(2s-1\). Adopting an optimization viewpoint, we minimize suitable penalty functions over the space of…
We present a novel algorithm to compute multi-scale curvature fields on triangle meshes. Our algorithm is based on finding robust mean curvatures using the ball neighborhood, where the radius of a ball corresponds to the scale of the…
The multiple scattering theory (MST) is one of the most widely used methods in electronic structure calculations. It features a perfect separation between the atomic configurations and site potentials, and hence provides an efficient way to…