In the paper, we consider a continuation approach for the binary quadratic program (BQP) based on a class of NCP-functions. More specifically, we recast the BQP as an equivalent minimization and then seeks its global minimizer via a global continuation method. Such approach had been considered in [11] which is based on the FischerBurmeister function. We investigate this continuation approach again by using a more general function, called the generalized FischerBurmeister function. However, the theoretical background for such extension can not be easily carried over. Indeed, it needs some subtle analysis.

Different from conventional spaceborne or airborne synthetic aperture radar (SAR) with optimal aperture length, an imaging radar with highly suboptimal aperture length acquires the data in short bursts by a geometry spreading over a large range. A polarlike or pseudopolar format grid is introduced to sample data close to the resolution, which presents the design of a separable kernel for efficient FFT implementation. The proposed imaging algorithm formulates the reflectivity image of the target scene as an interpolation-free double image series expansion with two usual approximation-induced phase error terms being taken into account, whereby more generalized application scenarios with high frequency, large bandwidth or larger aperture length for imaging a target scene located within either the far-field or the near-field of the radar aperture are processable with high accuracy. In addition, convergence

In this paper, a new type of finite difference Hermite weighted essentially non-oscillatory (HWENO) schemes are constructed for solving Hamilton-Jacobi (HJ) equations. Point values of both the solution and its first derivatives are used in the HWENO reconstruction and evolved via time advancing. While the evolution of the solution is still through the classical numerical fluxes to ensure convergence to weak solutions, the evolution of the first derivatives of the solution is through a simple dimension-by-dimension non-conservative procedure to gain efficiency. The main advantages of this new scheme include its compactness in the spatial field and its simplicity in the reconstructions. Extensive numerical experiments in one and two dimensional cases are performed to verify the accuracy, high resolution and efficiency of this new scheme.

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This is the first of a series of papers on the subject of projection methods for viscous incompressible flow calculations. The purpose of these papers is to provide a thorough understanding of the numerical phenomena involved in the projection methods, particularly when boundaries are present, and point to ways of designing more efficient, robust, and accurate numerical methods based on the primitive variable formulation. This paper contains the following topics: 1. convergence and optimal error estimates for both velocity and pressure up to the boundary; 2. explicit characterization of the numerical boundary layers in the pressure approximations and the intermediate velocity fields; 3. the effect of choosing different numerical boundary conditions at the projection step. We will show that a different choice of boundary conditions gives rise to different boundary layer structures. In particular, the straightforward Dirichlet boundary condition for the pressure leads to O(1) numerical boundary layers in the pressure and deteriorates the accuracy in the interior; and 4. postprocessing the numerical solutions to get more accurate approximations for the pressure.