Interpolation polynomial pn at the Chebyshev nodes cosπj/n (0 ≤ j ≤ n) for smooth functions is known to converge fast as n → ∞. The sequence {pn} is constructed recursively and efficiently in O(n log2 n) flops for each pn by using the FFT, where n is increased geometrically, n = 2i (i = 2, 3, . . . ), until an estimated error is within a given tolerance of ε. This sequence {2j}, however, grows ...

In this paper we present numerical methods for the nonlinear Schrödinger equations (NLS) in the semiclassical regimes: iε uεt = − ε 2 ∆u + V (x)u + f(|u|)u, x ∈ R, with nonzero far-field conditions. A time-splitting cosine-spectral (TS-Cosine) method is presented when the nonzero far-field conditions are or can be reduced to homogeneous Neumann conditions, a time-splitting Chebyshev-spectral (T...

In the present paper we give a characterization of Chebyshev subspaces in the space of (real or complex) continuously-differentiable functions of two variables. We also discuss various applications of the characterization theorem. Introduction. One of the central problems in approximation theory consists in determining the best approximation; that is, in a normed linear space X with a prescribe...

The power of density functional theory is often limited by the high computational demand in solving an eigenvalue problem at each self-consistent-field (SCF) iteration. The method presented in this paper replaces the explicit eigenvalue calculations by an approximation of the wanted invariant subspace, obtained with the help of well-selected Chebyshev polynomial filters. In this approach, only ...

The power of density functional theory is often limited by the high computational demand in solving an eigenvalue problem at each self-consistent-field (SCF) iteration. The method presented in this paper replaces the explicit eigenvalue calculations by an approximation of the wanted invariant subspace, obtained with the help of well-selected Chebyshev polynomial filters. In this approach, only ...