Restricted energy inequalities and numerical approximations

Restricted second random phase approximations and Tamm-Dancoff approximations for electronic excitation energy calculations.

In this article, we develop systematically second random phase approximations (RPA) and Tamm-Dancoff approximations (TDA) of particle-hole and particle-particle channels for calculating molecular excitation energies. The second particle-hole RPA/TDA can capture double excitations missed by the particle-hole RPA/TDA and time-dependent density-functional theory (TDDFT), while the second particle-...

Theory and Numerical Approximations

We consider a nonlinear Dirac system in one space dimension with periodic boundary conditions. First, we discuss questions on the existence and uniqueness of the solution. Then, we propose an implicit-explicit finite difference method for its approximation, proving optimal order a priori error estimates in various discrete norms and showing results from numerical experiments.

Generating Numerical Approximations

We describe a computational model for planning phrases like “more than a quarter” and “25.9 per cent” which describe proportions at different levels of precision. The model lays out the key choices in planning a numerical description, using formal definitions of mathematical form (e.g., the distinction between fractions and percentages) and roundness adapted from earlier studies. The task is mo...

Numerical Investigations of an Error Bound for Reduced Basis Approximations of Non-Coercice Variational Inequalities

We consider variational inequalities with different trial and test spaces and a possibly noncoercive bilinear form. Well-posedness has been shown under general conditions that are e.g. valid for the space-time formulation of parabolic variational inequalities. Fine discretizations for such problems resolve in large scale problems and thus in long computing times. To reduce the size of these pro...

Support Approximations Using Bonferroni-Type Inequalities