We present an efficient preconditioner for the orbital minimization method when the Hamiltonian is discretized using planewaves (i.e., pseudospectral method). This novel preconditioner is based on an approximate Fermi operator projection by pole expansion, combined with the sparsifying preconditioner to efficiently evaluate the pole expansion for a wide range of Hamiltonian operators. Numerical...

Computer-produced summaries have traditionally been evaluated by comparing them with human-produced summaries using the Fmeasure. However, the F-measure is not appropriate when alternative sentences are possible in a human-produced extract. In this paper, we examine some evaluation methods devised to overcome the problem, including utility-based evaluation. By giving scores for moderately impor...

The high-order accuracy of Fourier method makes it the method of choice in many large scale simulations. We discuss here the stability of Fourier method for nonlinear evolution problems, focusing on the two prototypical cases of the inviscid Burgers’ equation and the multi-dimensional incompressible Euler equations. The Fourier method for such problems with quadratic nonlinearities comes in two...

In this paper, a sixth order energy-conserved method is proposed for solving the three-dimensional time-domain Maxwell’s equations. Based on the method of lines, the spatial derivatives of the Maxwell’s equations are approximated with the aid of Fourier pseudo-spectral methods. The resulting ordinary differential equations can be cast as a canonical Hamiltonian system. Then, a fully-discretized...

An initial value problem with piecewise constant coe cients is considered. The accuracies for both nite di erence methods and the pseudospectral method are analyzed, and a modi cation of the initial value problem is suggested. The modi ed problem is shown to have the same temporal period as the original problem does, and a second order accuracy is obtained for the pseudospectral method at integ...

In this paper, error estimates for generalized Laguerre–Gauss-type interpolations are derived in nonuniformly weighted Sobolev spaces weighted with ωα,β(x) = x αe−βx, α > −1, β > 0. Generalized Laguerre pseudospectral methods are analyzed and implemented. Two model problems are considered. The proposed schemes keep spectral accuracy and, with suitable choice of basis functions, lead to sparse a...

This paper extends an earlier work [Appl. Math. Comput. 140 (2003) 77] to differential-algebraic equations with constraint singularities. Numerical solution of these problems is considered by pseudospectral method with domain decomposition and by giving a condition under which the general linear form problem can easily be transformed to the index reduced form by a simple formulation. Furthermor...

An efficient numerical method to compute solitary wave solutions to the free surface Euler equations is reported. It is based on the conformal mapping technique combined with an efficient Fourier pseudo-spectral method. The resulting nonlinear equation is solved via the Petviashvili iterative scheme. The computational results are compared to some existing approaches, such as Tanaka’s method and...

The Fourier pseudo-spectral method has been studied for a onedimensional coupled system of viscous Burgers equations. Two test problems with known exact solutions have been selected for this study. In this paper, the rate of convergence in time and error analysis of the solution of the first problem has been studied, while the numerical results of the second problem obtained by the present meth...

In this paper we present a very effective method for texture segmentation and analysis using a local spectral method. The idea is to use a modular pattern detection in textured images based on the use of a Pseudo-Wigner Distribution (PWD) followed by a decorrelation procedure that consists of a principal component analyzer (for texture segmentation). The goal is to combine the advantages of a h...