We reply to the Comment by Aryanpour, Maier, and Jarrell [Phys. Rev. B 71, 037101 (2005)] on our paper [Phys. Rev. B 65, 155112 (2002)]. We demonstrate, using general arguments and explicit examples, that whenever the correlation length is finite, local observables converge exponentially fast in the cluster size Lc within cellular dynamical mean field theory. This is a faster rate of convergenc...

Recently the nonlocal coherent-potential approximation (NLCPA) has been introduced by Jarrell and Krishnamurthy for describing the electronic structure of substitutionally-disordered systems. The NLCPA provides systematic corrections to the widely used coherent-potential approximation (CPA) whilst preserving the full symmetry of the underlying lattice. Here an analytical and systematic numerica...

As a model benchmark problem for this study we consider a highly singular transmission type eigenvalue problem which we study in detail both analytically as well as numerically. In order to justify our claim of cluster robust and highly accurate approximation of a selected groups of eigenvalues and associated eigenfunctions, we give a new analysis of a class of direct residual eigenspace/vector...

Sampling of 3D meshes is at the foundation of any surface simplification technique. In this paper, we use the recent results on quantization and surface approximation theory to propose a simple, robust, linear time, output sensitive algorithm for sampling meshes with the purpose of surface approximation. Our algorithm is based on the mapping of regular sampling and triangulation of the Gaussian...

Cluster Perturbation Theory (CPT) is a simple approximation scheme that applies to lattice models with local interactions, like the Hubbard model, or models where the local interaction is predominant. It proceeds by tiling the lattice into identical, finite-size clusters, solving these clusters exactly and treating the inter-cluster hopping terms at first order in strong-coupling perturbation t...

We introduce an extension of the dynamical mean-field approximation ~DMFA! that retains the causal properties and generality of the DMFA, but allows for systematic inclusion of nonlocal corrections. Our technique maps the problem to a self-consistently embedded cluster. The DMFA ~exact result! is recovered as the cluster size goes to 1 ~infinity!. As a demonstration, we study the Falicov-Kimbal...

The fission mechanism of multiply charged sodium clusters was investigated with molecular dynamics and a new potential featuring a local density approximation second-moment approach. We show that the critical size at which 2+, 3+ and 4+ charged clusters undergo fission due to Coulomb forces depends strongly on the cluster temperature. The smallest critical sizes occur for cold clusters. Master ...

We propose a new type of three-cluster equation which uses two-cluster resonating-groupmethod (RGM) kernels. In this equation, the orthogonality of the total wave-function to two-cluster Pauli-forbidden states is essential to eliminate redundant components admixed in the three-cluster systems. The explicit energy-dependence inherent in the exchange RGM kernel is self-consistently determined. Fo...

In this paper, we define and study q-statistical limit point, cluster q-statistically Cauchy, q-strongly Cesàro statistically C1q-summable sequences. We establish relationships of convergence with Further, apply to prove a Korovkin type approximation theorem.

This study proposes a method, designated as the GRP-index method, for the classification of continuous value datasets in which the instances do not provide any class information and may be imprecise and uncertain. The proposed method discretizes the values of the individual attributes within the dataset and achieves both the optimal number of clusters and the optimal classification accuracy. Th...