Super-resolution processing of passive millimeter-wave images based on conjugate-gradient algorithm

This paper designs a 3 mm radiometer and validate with experiments based on the principle of passive millimeter wave （PMMW） imaging. The poor spatial resolution, which is limited by antenna size, should be improved by post data processing. A conjugate-gradient （CG） algorithm is adopted to circumvent this drawback. Simulation and real data collected in laboratory environment are given, and the results show that the CG algorithm improves the spatial resolution and convergent rate. Further, it can reduce the ringing effects which are caused by regularizing the image restoration. Thus, the CG algorithm is easily implemented for PMMW imaging.

Conjugate-Gradient Progressive-Iterative Approximation for Loop and Catmull-Clark Subdivision Surface Interpolation

Loop and Catmull-Clark are the most famous approximation subdivision schemes,but their limit surfaces do not interpolate the vertices of the given mesh.Progressive-iterative approximation(PIA)is an efficient method for data interpolation and has a wide range of applications in many fields such as subdivision surface fitting,parametric curve and surface fitting among others.However,the convergence rate of classical PIA is slow.In this paper,we present a new and fast PIA format for constructing interpolation subdivision surface that interpolates the vertices of a mesh with arbitrary topology.The proposed method,named Conjugate-Gradient Progressive-Iterative Approximation(CG-PIA),is based on the Conjugate-Gradient Iterative algorithm and the Progressive Iterative Approximation(PIA)algorithm.The method is presented using Loop and Catmull-Clark subdivision surfaces.CG-PIA preserves the features of the classical PIA method,such as the advantages of both the local and global scheme and resemblance with the given mesh.Moreover,CG-PIA has the following features.1)It has a faster convergence rate compared with the classical PIA and W-PIA.2)CG-PIA avoids the selection of weights compared with W-PIA.3)CG-PIA does not need to modify the subdivision schemes compared with other methods with fairness measure.Numerous examples for Loop and Catmull-Clark subdivision surfaces are provided in this paper to demonstrate the efficiency and effectiveness of CG-PIA.

Optimization of a serpentine flow field with variable channel heights and widths for PEM fuel cells

The present study proposes a modified serpentine flow field design in which the channel heights vary along each straight flow path to enhance reactant transport and liquid water removal. An optimization approach, combining a simplified conjugate-gradient method (inverse solver) and a three-dimensional, two-phase, non-isothermal fuel cell model (direct solver), has been developed to optimize the key geometric parameters. The optimal design has tapered channels for channels 1, 3 and 4 and increasing heights for channels 2 and 5 with the flow widths first increasing and then decreasing. The optimal channel heights and widths enhance the efficiency by 22.51% compared with the basic design having all heights and widths of 1 mm. The diverging channels have a greater impact on cell performance than fine adjustments of the channel widths for the present simulation conditions. The channel heights have more effect on the sub-rib convection, while the channel widths affect the uniformity of the fuel delivery more. The reduced channel heights of channels 2–4 significantly enhance the sub-rib convection to effectively transport oxygen to and liquid water out of the diffusion layer. The final diverging channel prevents significant leakage of fuel to the outlet via sub-rib convection.

Linear response eigenvalue problem solved by extended locally optimal preconditioned conjugate gradient methods

The locally optimal block preconditioned 4-d conjugate gradient method(LOBP4dC G) for the linear response eigenvalue problem was proposed by Bai and Li(2013) and later was extended to the generalized linear response eigenvalue problem by Bai and Li(2014). We put forward two improvements to the method: A shifting deflation technique and an idea of extending the search subspace. The deflation technique is able to deflate away converged eigenpairs from future computation, and the idea of extending the search subspace increases convergence rate per iterative step. The resulting algorithm is called the extended LOBP4 dC G(ELOBP4dC G).Numerical results of the ELOBP4 dC G strongly demonstrate the capability of deflation technique and effectiveness the search space extension for solving linear response eigenvalue problems arising from linear response analysis of two molecule systems.

Error bounds of Lanczos approach for trust-region subproblem

Because of its vital role of the trust-region subproblem （TRS） in various applications, for example, in optimization and in ill-posed problems, there are several factorization-free algorithms for solving the large-scale sparse TRS. The truncated Lanczos approach proposed by N. I. M. Gould, S. Lucidi, M. Roma, and P. L. Toint [SIAM J. Optim., 1999, 9： 504-525] is a natural extension of the classical Lanczos method for the symmetric linear system and eigenvalue problem and, indeed follows the classical Rayleigh-Ritz procedure for eigenvalue computations. It consists of 1） projecting the original TRS to the Krylov subspa^es to yield smaller size TRS＇s and then 2） solving the resulted TRS＇s to get the approximates of the original TRS. This paper presents a posterior error bounds for both the global optimal value and the optimal solution between the original TRS and their projected counterparts. Our error bounds mainly rely on the factors from the Lanczos process as well as the data of the original TRS and, could be helpful in designing certain stopping criteria for the truncated Lanczos approach.