We present a subspace projection technique to conduct large-scale Kohn-Sham density functional theory calculations using higher-order spectral finite-element discretization. The proposed method treats both metallic and insulating materials in a single framework, and is applicable to both pseudopotential as well as all-electron calculations. The key ideas involved in the development of this meth...

Calculating the spectral function of two dimensional systems is arguably one most pressing challenges in modern computational condensed matter physics. While efficient techniques are available lower dimensions, present insurmountable hurdles, ranging from sign problem quantum Monte Carlo (MC), to entanglement area law tensor network based methods. We hereby a variational approach on Chebyshev e...

In this paper, a two-dimensional multi-wavelet is constructed in terms of Chebyshev polynomials. The constructed multi-wavelet is an orthonormal basis for space. By discretizing two-dimensional Fredholm integral equation reduce to a algebraic system. The obtained system is solved by the Galerkin method in the subspace of by using two-dimensional multi-wavelet bases. Because the bases of subs...

We study weakly continuously Urysohn spaces, which were introduced in [Z]. We show that every weakly continuously Urysohn w∆-space has a base of countable order, that separable weakly continuously Urysohn spaces are submetrizable, hence continuously Urysohn, that monontonically normal weakly continuously Urysohn spaces are hereditarily paracompact, and that no linear extension of any uncountabl...

In this paper, we derive an explicit formula for the bivariate Lagrange basis polynomials of a general set checkerboard nodes. This generalizes existing results at Padua nodes, Chebyshev Morrow-Patterson and Geronimus We also construct subspace spanned by linearly independent vanishing that vanish nodes prove uniqueness in quotient space defined as with certain degree over polynomials.

The electron spin resonance (ESR) of nanoscale molecular magnet V15 is studied. Since the Hamiltonian of V15 has a large Hilbert space and numerical calculations of the ESR signal evaluating the Kubo formula with exact diagonalization method is difficult, we implement the formula with the help of the random vector technique and the Chebyshev polynominal expansion, which we name the double Cheby...

Abstract. This paper discusses a method based on Laguerre polynomials combined with a Filtered Conjugate Residual (FCR) framework to compute the product of the exponential of a matrix by a vector. The method implicitly uses an expansion of the exponential function in a series of orthogonal Laguerre polynomials, much like existing methods based on Chebyshev polynomials do. Owing to the fact that...

In this paper a new technique is proposed for the clustering and classification of spatio-temporal object trajectories extracted from video motion clips. The trajectories are represented as motion time series and modelled using Chebyshev polynomial approximations. Trajectory clustering is then performed to discover patterns of similar object motion. The coefficients of the basis functions are u...

We prove that if X is a subspace of Lp (2 < p < ∞), then either X embeds isomorphically into `p ⊕ `2 or X contains a subspace Y, which is isomorphic to `p(`2). We also give an intrinsic characterization of when X embeds into `p⊕`2 in terms of weakly null trees in X or, equivalently, in terms of the “infinite asymptotic game” played in X. This solves problems concerning small subspaces of Lp ori...

When solving the Symmetric Positive Definite (SPD) linear system Ax = b with the conjugate gradient method, the smallest eigenvalues in the matrix A often slow down the convergence. Consequently if the smallest eigenvalues in A could be somehow “removed”, the convergence may be improved. This observation is of importance even when a preconditioner is used, and some extra techniques might be inv...