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Proceedings of the 34th International conference on Neural Information Processing Systems

作者： Agniva Chowdhury Palma London Haim Avron Petros Drineas Department of Statistics Purdue University West Lafayette IN ORIE Department Cornell University Ithaca NY School of Mathematical Sciences Tel Aviv University Tel Aviv Israel Department of Computer Science Purdue University West Lafayette IN

ISBN: (纸本)9781713829546

linear programming (LP) is used in many machine learning applications, such as ℓ1-regularized SVMs, basis pursuit, nonnegative matrix factorization, etc. Interior Point methods (IPMs) are one of the most popular methods to solve LPs both in theory and in practice. Their underlying complexity is dominated by the cost of solving a system of linear equations at each iteration. In this paper, we consider infeasible IPMs for the special case where the number of variables is much larger than the number of constraints (i.e., wide), or vice-versa (i.e., tall) by taking the dual. Using tools from Randomized linear algebra, we present a preconditioning technique that, when combined with the Conjugate Gradient iterative solver, prov-ably guarantees that infeasible IPM algorithms (suitably modified to account for the error incurred by the approximate solver), converge to a feasible, approximately optimal solution, without increasing their iteration complexity. Our empirical evaluations verify our theoretical results on both real and synthetic data.

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A General Test for the linear Structure of Covariance Matrices of Gaussian Populations

A General Test for the Linear Structure of Covariance Matric...

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IEEE International conference on Acoustics, Speech and Signal Processing

作者： Yu-Hang Xiao David Ramirez Peter J. Schreier Signal and System Theory Group University of Paderborn Germany Dept. of Signal Theory and Communications Universidad Carlos III de Madrid Spain

ISBN: (数字)9781509066315

ISBN: (纸本)9781509066315;9781509066322

This paper addresses the problem of testing whether a covariance matrix can be expressed by an unknown linear combination of a set of known matrices or by another unknown linear combination of a set of different, but known, matrices. This problem is of interest in a wide range of real-world applications, such as radar, sonar, and spectrum sensing. We study the problem under the Gaussian assumption and derive the generalized likelihood ratio test (GLRT). Since there is no general closed-form solution for the maximum likelihood (ML) estimates of the covariance matrices, which are required for the GLRT, we resort to a powerful inverse iteration algorithm. Finally, an example, along with numerical results, is given to illustrate the methodology.

关键词： covariance matrices iterative methods maximum likelihood estimation signal detection

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Nonlinear static FE-analysis of smart piezolaminated FGM shells at finite rotations 7th

Nonlinear static FE-analysis of smart piezolaminated FGM she...

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7th International conference on Structural Engineering, Mechanics and Computation (SEMC)

作者： Schmidt, R. Rao, M. N. Schroeder, K-U Rhein Westfal TH Aachen Inst Struct Mech & Lightweight Design Aachen Germany

ISBN: (纸本)9780429426506;9781138386969

The purpose of this work is to investigate the static behavior of piezolaminated thin-walled functionally graded material (FGM) and composite shells in the range of geometrically linear and nonlinear deformations. A power law type variation of FGM material properties is adopted. Finite rotations and full nonlinear terms in the geometrically nonlinear strain-displacement relations are considered in the framework of FOSD theory to derive the variational formulation. In order to enrich the behavior and reliability of the four-node piezolaminated composite shell element, an assumed natural strain (ANS) method for the shear strains, an enhanced assumed strain (EAS) method for the membrane strains and an enhanced assumed gradient (EAG) method for the electric field is encompassed. Predictive capabilities of the proposed numerical formulation are demonstrated using several numerical examples, in particular shells integrated with piezolayers in both sensory and actuator applications in the range of linear and geometrically nonlinear deformations. numerical simulations with the present model and other simplified nonlinear models available in literature are performed and compared, demonstrating the worthiness of the present method in large deflection analysis. Additionally, the present results are compared with those obtained by Abaqus by modeling the master structure using the shell S8R element and piezo-layers using C3D20RE solid elements.

关键词： numerical methods

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Stresses in a pressurised parabolic ogival toroidal vessel 7th

Stresses in a pressurised parabolic ogival toroidal vessel

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7th International conference on Structural Engineering, Mechanics and Computation (SEMC)

作者： Enoma, N. Zingoni, A. Univ Cape Town Dept Civil Engn Struct Engn & Mech Grp Cape Town South Africa

ISBN: (纸本)9780429426506;9781138386969

A closed-form analytical solution is presented for the complete determination of the stress state and deformations within parabolic ogival toroidal vessels under internal pressure. linear theory-equations for the vessels are formulated on the basis of the theory of thin-shells of revolution. The equations are simplified and systematically solved using the general strategy of Zingoni (2018), in which the Geckeler approximations are adopted, and the membrane solution is superimposed with an approximate bending solution of the bending-theory equations. The accuracy of the developed solution algorithm is demonstrated through a numerical example by comparing results with those from finite element analysis. Excellent agreement is achieved throughout the vessel. The accuracy of the developed method demonstrates the validity of Geckeler approximations even in the anticlastic surfaces of shells of revolution.

关键词： numerical methods

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On solving the geometrically nonlinear and linear problems of transverse bending of a hinged fixing sandwich plate with transversally soft core 12

On solving the geometrically nonlinear and linear problems o...

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12th International conference on Mesh methods for Boundary - Value Problems and applications

作者： Makarov, M. V. Badriev, I. B. Buyanov, V. Yu Smirnova, E. V. Kazan Fed Univ 18 Kremlyovskaya St Kazan 420008 Russia Kazan Natl Res Tech Univ 10 K Marks St Kazan 420111 Russia

The study of the problem of finding the stress-strain state of a sandwich plate with a transversally soft core under the action of a transverse load in a one-dimensional geometrically nonlinear formulation was carried out. A generalized formulation of the problem in the form of an operator equation is proposed. The properties of the operator of the equation are established, which make it possible to use the general results of the theory of monotone operators in the study of correctness. To find the stress-strain state of the plate, a two-layer iterative method is proposed with lowering the nonlinearity on the lower layer. A finite-dimensional approximation of the problem and the iterative method was carried out. The convergence of finite-dimensional approximations and the iterative method has been studied. For the numerical implementation of the proposed approximate methods, a software package has been developed in the Matlab environment. Based on it, numerical experiments were carried out.

关键词： Iterative methods

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On transmutation operators and neumann series of bessel functions representations for solutions of linear higher order differential equations

On transmutation operators and neumann series of bessel func...

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International Scientific conference of Modern methods and Problems of Operator theory and Harmonic Analysis and Their applications, OTHA 2018

作者： Gómez, Flor A. Kravchenko, Vladislav V. Departamento de Matemáticas Cinvestav Unidad Querétaro Juriquilla Mexico Regional Mathematical Center of Southern Federal University Rostov-on-Don Russia

ISBN: (纸本)9783030267476

A new representation for solutions of linear higher order ordinary differential equations with a spectral parameter is obtained in terms of Neumann series of Bessel functions. The result is based on a Fourier-Legendre series representation for the Borel transform of the solution with respect to the spectral parameter. Estimates for the coefficients and for the convergence of the representation are derived. numerical illustrations of the applicability of the obtained formulae are presented. © Springer Nature Switzerland AG 2019.

关键词： Bessel functions

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numerical Analysis for Applied Science, Second Edition 2

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丛书名： Pure and applied mathematics

2019年

作者： Myron B. Allen Eli L. Isaacson

ISBN: (数字)9781119245476

ISBN: (纸本)9781119245469

Pragmatic and Adaptable Textbook Meets the Needs of Students and Instructors from Diverse Fields numerical analysis is a core subject in data science and an essential tool for applied mathematicians, engineers, and physical and biological scientists. This updated and expanded edition of numerical Analysis for Applied Science follows the tradition of its precursor by providing a modern, flexible approach to the theory and practical applications of the field. As before, the authors emphasize the motivation, construction, and practical considerations before presenting rigorous theoretical analysis. This approach allows instructors to adapt the textbook to a spectrum of uses, ranging from one-semester, methods-oriented courses to multi-semester theoretical courses. The book includes an expanded first chapter reviewing useful tools from analysis and linear algebra. Subsequent chapters include clearly structured expositions covering the motivation, practical considerations, and theory for each class of methods. The book includes over 250 problems exploring practical and theoretical questions and 32 pseudocodes to help students implement the methods. Other notable features include: A preface providing advice for instructors on using the text for a single semester course or multiple-semester sequence of courses Discussion of topics covered infrequently by other texts at this level, such as multidimensional interpolation, quasi-Newton methods in several variables, multigrid methods, preconditioned conjugate-gradient methods, finite-difference methods for partial differential equations, and an introduction to finite-element theory New topics and expanded treatment of existing topics to address developments in the field since publication of the first edition More than twice as many computational and theoretical exercises as the first edition. numerical Analysis for Applied Science, Second Edition provides an excellent foundation for graduate and advanced undergraduate cours

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Approximation of fuzzy functions by fuzzy interpolating bicubic splines: 2018 CMMSE conference

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JOURNAL OF MATHEMATICAL CHEMISTRY 2019年第5期57卷 1252-1267页

作者： Gonzalez, P. Idais, H. Pasadas, M. Yasin, M. Univ Granada Dept Matemat Aplicada E-18071 Granada Spain

One of the most interesting and important techniques in applied mathematics is interpolation and approximation. It can be also shown that basic theory of fuzzy sets and operations with fuzzy numbers can be used, and result very convenient, for solving many analytical chemistry problems: as depth profile comparison or calibration with errors in signals and/or concentrations, for spectra interpretation, or even for automatic qualitative analysis or expert systems with X-ray spectroscopy. In this special context, we introduce in this paper a new fuzzy interpolation method of fuzzy data or functions, specially indicated in all these chemical applications. We will use bicubic splines (cubic splines of two variables) of class C2 as linear combinations of a basis constructed by a tensor product of univariate B-splines in each of these variables. First we establish a bicubic interpolation spline method of a given fuzzy data set or a given fuzzy bivariate function. We proof the existence of a unique solution of this problem and we show a convergence result. Finally, we test the effectiveness of this method by some numerical and graphical examples.

关键词： Interpolation and approximation Fuzzy data Bicubic splines Analytical chemistry Calibration Spectroscopy

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Network Density of States 19

Network Density of States

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25th ACM SIGKDD International conference on Knowledge Discovery & Data Mining (KDD)

作者： Dong, Kun Benson, Austin R. Bindel, David Cornell Univ Ithaca NY 14850 USA

ISBN: (纸本)9781450362016

Spectral analysis connects graph structure to the eigenvalues and eigenvectors of associated matrices. Much of spectral graph theory descends directly from spectral geometry, the study of differentiable manifolds through the spectra of associated differential operators. But the translation from spectral geometry to spectral graph theory has largely focused on results involving only a few extreme eigenvalues and their associated eigenvalues. Unlike in geometry, the study of graphs through the overall distribution of eigenvalues - the spectral density - is largely limited to simple random graph models. The interior of the spectrum of real-world graphs remains largely unexplored, difficult to compute and to interpret. In this paper, we delve into the heart of spectral densities of real-world graphs. We borrow tools developed in condensed matter physics, and add novel adaptations to handle the spectral signatures of common graph motifs. The resulting methods are highly efficient, as we illustrate by computing spectral densities for graphs with over a billion edges on a single compute node. Beyond providing visually compelling fingerprints of graphs, we show how the estimation of spectral densities facilitates the computation of many common centrality measures, and use spectral densities to estimate meaningful information about graph structure that cannot be inferred from the extremal eigenpairs alone.

关键词： spectral graph theory numerical linear algebra

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numerical STUDY ON THE TEMPORAL DISCRETIZATION SCHEMES IN TWO-PHASE WAVE SIMULATION 38

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38th ASME International conference on Ocean, Offshore and Arctic Engineering (OMAE 2019)

作者： Kim, Young Jun Bouscasse, Benjamin Seng, Sopheak Le Touze, David Ecole Cent Nantes CNRS UMR 6598 Nantes France Bur Veritas Paris La Defense France

ISBN: (纸本)9780791858776

The generation and propagation of waves in a viscous flow solver are indispensable part of naval computational fluid dynamic (CFD) applications. This paper presents numerical simulations of two-dimensional wave propagation in the framework of two-phase finite volume method (FVM) with different temporal discretization schemes. Implicit Euler, Crank-Nicolson(CN) and second-order backward temporal discretization schemes are compared by using viscous flow solver based on the open source library OpenFOAM. The combinations of each temporal discretization scheme and explicit limiter are used for the formulation of the Volume Of Fluid (VOF) field convection equation. A new formulation using the second-order backward temporal discretization scheme with explicit limiter are investigated. Twodimensional periodic domains are considered to compare different time -stepping methods. Also, five different refinement levels of meshes are used to study the convergence properties of each method. The non-linear wave is generated with stream function wave theory using 'foamStar', which is a specialized Open FOAM library package developed by Bureau Veritas in collaboration with Ecole Centrale de Nantes.

关键词： Wave propagation Fluids Computer simulation Simulation Waves Viscous flow Wave theory of light Computational fluid dynamics Convection Finite volume methods Nonlinear waves Collaboration

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