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Matrix completion is about recovering a matrix from its partial revealed entries, and it can often be achieved by exploiting the inherent simplicity or low dimensional structure of the target matrix. For instance, a typical notion of matrix simplicity is low rank. In this paper we study matrix completion based on another low dimensional structure, namely the low rank Hankel structure in the Fourier domain. It is shown that matrices with this structure can be exactly recovered by solving a convex optimization program provided the sampling complexity is nearly optimal. Empirical results are also presented to justify the effectiveness of the convex method. [ABSTRACT FROM AUTHOR]

For linear and nonlinear systems arising from the discretization of PDEs, multiplicative Schwarz preconditioners can be defined based on subsets of the unknowns that derive from domain decomposition, field splitting, or other collections of conveniently solved subproblems, and are well established theoretically for nonoverlapping subsets. For overlapping subsets, establishing the equivalence of the preconditioned and original iterations is less trivial. We derive herein an explicit formulation for a variety of multiplicative Schwarz preconditioners including overlaps representative of interfacial and bulk coupling in multiphysics systems, thus extending theoretical support for the nonlinear multiplicative Schwarz preconditioned inexact Newton (MSPIN) algorithm to these classes. For nonlinear multiplicative Schwarz preconditioners with overlaps, we illustrate the performance through numerical experiments involving applications such as a shocked duct flow and a natural convection cavity flow. We begin with a broad introduction to nonlinear preconditioning to set the context for those new to the technique. • New theory is provided for multiplicative Schwarz preconditioning for partitions typical of interface or bulk coupling in multiphysics problems. • Effects of subdomain and field overlapping on the convergence of the MSPIN nonlinear preconditioner are illustrated with numerical examples. • Left and right sided, additive and multiplicative, nonoverlapping and overlapping, linear and nonlinear Schwarz preconditioners are compared. [ABSTRACT FROM AUTHOR]

This paper presents an efficient algorithmic implementation of the iterative minimization formulation (IMF) for fast local search of transition state on potential energy surface. The IMF is a second order iterative scheme providing a general and rigorous description for the eigenvector-following (min-mode following) methodology. We offer a unified interpretation in numerics via the IMF for existing eigenvector-following methods, such as the gentlest ascent dynamics, the dimer method and many other variants. We then propose our new algorithm based on the IMF. The main feature of our algorithm is that the translation step is replaced by solving an optimization subproblem associated with an auxiliary objective function which is constructed from the min-mode information. We show that using an efficient scheme for the inexact solver and enforcing an adaptive stopping criterion for this subproblem, the overall computational cost will be effectively reduced and a super-linear rate between the accuracy and the computational cost can be achieved. A series of numerical tests demonstrate the significant improvement in the computational efficiency for the new algorithm. [ABSTRACT FROM AUTHOR]

To develop a visual and reliable weld quality assessment method for resistant spot welding, the electrode displacement signal was measured and analyzed. Some statistical features closely related to the weld quality were extracted. The multi-dimensional extracted features from the signal were sketched as Chernoff face which characterizes the welding quality through the different facial expressions. The weld quality was summarized as four levels, namely poor, good, excellent and expulsion, and each level corresponded to one kind of facial expression. By visual judgment, good or bad welds were identified accurately and rapidly even though the weld was made under abnormal welding conditions. In particular, the visual characteristic makes the diagnostic procedure for welding quality easily understood and interpreted. [ABSTRACT FROM AUTHOR]

Abstract: Plane wave pseudopotential (PWP) density functional theory (DFT) calculation is the most widely used method for material simulations, but its absolute speed stagnated due to the inability to use large scale CPU based computers. By a drastic redesign of the algorithm, and moving all the major computation parts into GPU, we have reached a speed of 12s per molecular dynamics (MD) step for a 512 atom system using 256GPU cards. This is about 20 times faster than the CPU version of the code regardless of the number of CPU cores used. Our tests and analysis on different GPU platforms and configurations shed lights on the optimal GPU deployments for PWP-DFT calculations. An 1800 step MD simulation is used to study the liquid phase properties of GaInP. [Copyright &y& Elsevier]