On exact and approximate exchange-energy densities

Kinetic and Exchange Energy Densities near the Nucleus

We investigate the behavior of the kinetic and the exchange energy densities near the nuclear cusp of atomic systems. Considering hydrogenic orbitals, we derive analytical expressions near the nucleus, for single shells, as well as in the semiclassical limit of large non-relativistic neutral atoms. We show that a model based on the helium iso-electronic series is very accurate, as also confirme...

Exact and approximate . . .

Exact and Approximate Bandwidth

In this paper we gather several improvements in the field of exact and approximate exponential-time algorithms for the BANDWIDTH problem. For graphs with treewidth t we present a O(n2) exact algorithm. Moreover for the same class of graphs we introduce a subexponential constant-approximation scheme – for any α > 0 there exists a (1 + α)-approximation algorithm running in O(exp(c(t + √ n/α) log ...

Improving on exact tests by approximate conditioning

The often conservative nature, for discrete data, of so-called exact tests seems usually the result of unnecessarily precise conditioning. We consider avoiding this by conditioning only approximately on the sufficient statistics for nuisance parameters. Modest relaxation of conditioning results in small loss in terms of the rationale for conditional inference, but can greatly reduce the difficu...

Approximate Versus Exact Equilibria∗

This paper develops theoretical foundations for an error analysis of approximate equilibria in dynamic stochastic general equilibrium models with heterogeneous agents and incomplete financial markets. While there are several algorithms which compute prices and allocations for which agents’ first order conditions are approximately satisfied (‘approximate equilibria’), there are few results on ho...