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作者： Nguyen, Nam Needell, Deanna Woolf, Tina IBM Thomas J. Watson Research Yorktown HeightsNY10598 United States Claremont McKenna College ClaremontCA91711 United States Claremont Graduate University ClaremontCA91711 United States

Motivated by recent work on stochastic gradient descent methods, we develop two stochastic variants of greedy algorithms for possibly non-convex optimization problems with sparsity constraints. We prove linear convergence1 in expectation to the solution within a specified tolerance. This generalized framework is specialized to the problems of sparse signal recovery in compressed sensing and low-rank matrix recovery, giving methods with provable convergence guarantees that often outperform their deterministic counterparts. We also analyze the settings, where gradients and projections can only be computed approximately, and prove the methods are robust to these approximations. We include many numerical experiments, which align with the theoretical analysis and demonstrate these improvements in several different settings. © 2017 IEEE.

关键词： Compressed sensing

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AN OPTIMAL Q-OR KRYLOV SUBSPACE METHOD FOR SOLVING linear SYSTEMS

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ELECTRONIC TRANSACTIONS ON numerical ANALYSIS 2017年 47卷 127-152页

作者： Meurant, Gerard 30 Rue Sergent Bauchat F-75012 Paris France

Today the most popular iterative methods for solving nonsymmetric linear systems are Krylov methods. In this paper we show how to construct a non-orthogonal basis of the Krylov subspace such that the quasi-orthogonal residual (Q-OR) Krylov method using this basis yields the same residual norms as GMRES up to the final stagnation phase, provided GMRES is not stagnating. In many examples this new Krylov method gives a better maximum attainable accuracy than GMRES with a modified Gram-Schmidt (MGS) implementation. Even though the number of floating point operations per iteration is larger than for GMRES, the optimal Q-OR method offers more potential for parallelism than GMRES with MGS.

关键词： linear systems Krylov methods Q-OR algorithm

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Sampling Type Reconstruction Processes for the Disk algebra

Sampling Type Reconstruction Processes for the Disk Algebra

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International conference on Sampling theory and applications

作者： Holger Boche Volker Pohl Lehrstuhl fur Theoretische Informationstechnik Technische Universitat Munchen

ISBN: (纸本)9781538615669

This paper considers the classical problem of recovering functions in the disk algebra from discrete samples taken at the unit circle by means of linear sampling type approximation methods. The paper characterizes subspaces of the disk algebra on which linear approximation operators do exist and subspaces on which such operators do not exist. The subspaces on which a linear signal recovery is possible are characterized by a sufficient concentration of the signal energy in the low frequency components of the signal.

关键词： Disk algebra Sampling Uniform recovery

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Vertical wave loads acting on a cruise ship in head, oblique and following regular waves 6th

Vertical wave loads acting on a cruise ship in head, oblique...

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6th International conference on Marine Structures, MARSTRUCT 2017

作者： Rajendran, S. Guedes Soares, C. Instituto Superior Técnico Universidade de Lisboa Lisbon Portugal

ISBN: (纸本)9781138069077

The vertical shear force and bending moment acting on a cruise ship in moderate to large amplitude regular waves are calculated using a body nonlinear time domain method based on strip theory. The Froude-Krylov and hydrostatic forces are calculated for the exact wetted surface under the incident wave profile for each time step. Frequency dependent coefficients are used for calculation of the radiation forces. The radiation forces are linear and are calculated for mean water level. The ship responses in different headings are numerically analysed and compared with experimental results obtained from a wave tank. The main objective of this paper is to conduct a preliminary investigation on the applicability of the developed numerical method for calculation of loads in different headings for practical engineering applications. © 2017 Taylor & Francis Group, London.

关键词： numerical methods

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Scientific computations on multi-core systems using different programming frameworks

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APPLIED numerical MATHEMATICS 2016年 104卷 62-80页

作者： Michailidis, Panagiotis D. Margaritis, Konstantinos G. Univ Macedonia Dept Balkan Slav & Oriental Studies 156 Egnatia Str Thessaloniki 54636 Greece Univ Macedonia Dept Appl Informat 156 Egnatia Str Thessaloniki 54636 Greece

numerical linear algebra is one of the most important forms of scientific computation. The basic computations in numerical linear algebra are matrix computations and linear systems solution. These computations are used as kernels in many computational problems. This study demonstrates the parallelisation of these scientific computations using multi core programming frameworks. Specifically, the frameworks examined here are Pthreads, OpenMP, Intel Cilk Plus, Intel TBB, SWARM, and FastFlow. A unified and exploratory performance evaluation and a qualitative study of these frameworks are also presented for parallel scientific computations with several parameters. The OpenMP and SWARM models produce good results running in parallel with compiler optimisation when implementing matrix operations at large and medium scales, whereas the remaining models do not perform as well for some matrix operations. The qualitative results show that the OpenMP, Cilk Plus, TBB, and SWARM frameworks require minimal programming effort, whereas the other models require advanced programming skills and experience. Finally, based on an extended study, general conclusions regarding the programming models and matrix operations for some parameters were obtained. (C) 2014 IMACS. Published by Elsevier B:V. All rights reserved.

关键词： Scientific computations linear algebra Parallel computing Multi-core Parallel programming

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Implementing mathematical models for singular integrals 3

Implementing mathematical models for singular integrals

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3rd International conference on numerical and Symbolic Computation: Developments and applications, SYMCOMP 2017

作者： Martins, Paula Ventura Conceicąõ, Ana C. Research Centre of Spatial and Organizational Dynamics Faculdade de Ciências e Tecnologia Universidade Do Algarve Faro8005-139 Portugal Center for Functional Analysis Linear Structures and Applications Faculdade de Ciências e Tecnologia Universidade Do Algarve Faro8005-139 Portugal

ISBN: (纸本)9789899941038

In recent years, several software applications with extensive capabilities of symbolic computation had been available to the general public. These applications, known as computer algebra systems (CAS), allow to delegate to a computer all, or a significant part, of the symbolic calculations present in many mathematical algorithms. A mathematical model is a description of a system using mathematical concepts and language. Mathematical models are used in natural sciences and engineering, as well as in social sciences. The main goal of this work is to provide a simple and efficient textual language to formalize mathematical models in the domain of singular integrals. In other words, a mathematician may wish to formulate problems using a computer language specialized to this particular application domain. This new language to compute singular integrals (also known as a Domain-Specific Language-DSL) will not have the complexity that is normally found in general-purpose languages like C, Java and Python. With Xtext and Eclipse, the authors will create a syntax highlighting, error checking and auto-completion editor for singular integrals. To show the effectiveness of the proposed language, a test case is presented with the model of the [SInt] algorithm that computes Cauchy type singular integrals. © ECCOMAS, Portugal.

关键词： Problem oriented languages

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Inverse methods For Computational Simulations And. Optimization Of Erosion Models In Power Plants 58

Inverse Methods For Computational Simulations And. Optimizat...

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58th IEEE International Scientific conference on Power and Electrical Engineering of Riga-Technical-University (RTUCON)

作者： Casesnoves, Francisco Surzhenkov, Andrei Tallinn Univ Technol Ehitajate Tee 5 EE-19086 Tallinn Estonia Tallinn Univ Technol Dept Mech & Ind Engn Ehitajate Tee 5 EE-19086 Tallinn Estonia

ISBN: (纸本)9781538638460

Simulations and linear/Nonlinear Optimization mathematical methods constitute presently the choice of preference in getting improvements for erosion and corrosion simulations/determinations in general tribology, hiotribology and tribocorrosion. This criterion is also applicable for engineering reliability functional efficacy/efficiency during energy-power plants lifetime with important consequences in the probabilities of operating failure of power-plant. Their running essential parts study control is carried out with the necessary tribotests for the definite validation of the models specifically considered in their mechanical electromechanical-systems. In previous contributions, an extent review of erosion and con-osion models applicable on energy power plants machinery was presented. In this new contribution a subsequent research stage towards formal simulation and optimization of those models is shown. In other words, Inverse Applied methods, earned out computationally, are used in modem mathematical approaches for accurate selection/fitting of the optimized modeling results, fact that happens in a large number of science-engineering branches, and also in energy power plants operation. Stepping forward in this research-line, this article deals with initial programming simulations series of selected model formulations, and mathematical analysis in new graphical simulation optimization methods. In doing so, subsequently nonlinear optimization programming techniques are developed, to conclude with the presentation of a hardface metal-coatings design for W-Co composites types. That model overview is related to experimental abrasive-erosion Mbotests performed at laboratory. The deliberation of the second generation of functional tribology models was detailed with computational-mathematical scopes. Finally, an objective discussion of the numerical results and datalgraphs series was presented in summary.

关键词： power engineering functional power-plants nonlinear optimization inverse problems theory/applications engineering reliability operational probabilities

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A parallel sparse linear system solver based on Hermitian/skew-Hermitian splitting

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COMPUTERS & MATHEMATICS WITH applications 2016年第8期72卷 2000-2007页

作者： Zhang, Zhengyi Sameh, Ahmed H. Purdue Univ Dept Comp Sci 305 N Univ St W Lafayette IN 47907 USA

In this paper we describe a parallel algorithm for solving large sparse nonsingular linear systems Ax = f, of order n, using the Hermitian Skew-Hermitian splitting approach for handling the augmented linear system, of order 2n, that arises from the linear least problem of minimizing the 2-norm of (f-Ax). We use the restarted GMRES as the outer iteration with the Hermitian Skew-Hermitian Splitting (HSS) preconditioner. In solving systems involving this preconditioner, the most time consuming part deals with handling shifted skew-symmetric systems. We solve such systems using the successive overrelaxation (SOR). Theoretical analysis shows that our solver always converges to the unique solution of Ax = f. We present several numerical experiments that demonstrate the robustness of our solver compared to other schemes, and show its parallel scalability on a single multicore node. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： numerical linear algebra Krylov subspace methods Preconditioners Hermitian/Skew-Hermitian splitting Parallel numerical algorithms

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Eigenvalue-eigenvector structure of Schoenmakers-Coffey matrices via Toeplitz technology and applications

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linear algebra AND ITS applications 2016年 491卷 138-160页

作者： Salinelli, E. Serra-Capizzano, S. Sesana, D. Univ Piemonte Orientale Amedeo Avogadro Alessandr Dipartimento Studi Econ & Impresa Via Perrone 18 I-28100 Novara Italy Univ Insubria Dipartimento Sci & Alta Tecnol Via Valleggio 11 I-22100 Como Italy Uppsala Univ Dept Informat Technol Box 337 SE-75105 Uppsala Sweden

The paper is concerned with the spectral properties of Green matrices and of a special subclass of the latter, known as Schoenmakers-Coffey matrices, which have a role in financial applications. The main results are related to the eigenvalue distribution of sequences of Green matrices of increasing size, while for the subclass of interest mentioned above, we also study the eigenvector oscillation structure: interestingly enough, even if these matrices are not shift invariant (Toeplitz), the results are obtained by using tools coming from Toeplitz technology. Indeed, for the asymptotic spectral distribution analysis, we use the theory of Generalized Locally Toeplitz sequences, while techniques taken from the study of Kac-Murdoch-Szego matrices (again connected to Toeplitz matrices) are employed for the eigenvector oscillation structure results of the Schoenmakers-Coffey matrices. Few numerical tests are reported in order to illustrate the theoretical findings. (C) 2015 Elsevier Inc. All rights reserved.

关键词： Schoenmakers-Coffey matrices Green matrices Tridiagonal matrices Spectral distribution GLT sequence Eigenvector oscillations

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Study on the response of elastomeric bearings with 3d numerical simulations and experimental validation 6

Study on the response of elastomeric bearings with 3d numeri...

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6th International conference on Computational methods in Structural Dynamics and Earthquake Engineering, COMPDYN 2017

作者： Forcellini, D. Mitoulis, S. Kalfas, K.N. Università di San Marino Via Salita alla Rocca 44 San Marino47890 United States University of Surrey Stag Hill Campus GuildfordGU2 7XH United Kingdom COSTAIN Engineering and Construction Limited London Bridge Station Redevelopment 82 St Thomas Street LondonSE1 3QU United Kingdom

ISBN: (纸本)9786188284418

Multi-layer elastomeric bearings are used as common means of isolation with a large number of applications over the last 20 years in infrastructure assets. In this regard, seismic isolation is one of the most promising design philosophies for protecting structures against the catastrophic effects of earthquakes. Isolated bridges should be designed to respond with minimal or no damage (i.e. essentially elastic behavior). Additionally, in isolated bridges seismically induced damage is expected to be concentrated within the isolators, which are designed to be easily replaced. Thus, isolated bridges are resilient structures as their design is aligned to the principles of resilience, i.e. low-damage and quick restoration. Elastomeric bearings can be subjected to large axial loads and /shear displacements during strong earthquakes, which may also induce buckling effects. The recent Forcellini and Kelly (2014) model for elastomeric bearings allows to take into account large deformation response of a bearing when buckling occurs. This paper aims to identify the accuracy of this theory using experimental results and detailed numerical simulations carried out on ABAQUS. The finite element (FE) model has been reproduced with a layered system able to represent the alternating steel and rubber layers and the bolted connections. The presented FE model can be used as a powerful tool for predicting the non-linear behaviors registered during the lab tests. This study will provide new insights useful to designers, engineers and consultants.

关键词： Finite element method

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