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11th International conference on High Performance Computing for Computational Science, VECPAR 2014

ISBN: (纸本)9783319173528

The proceedings contain 25 papers. The special focus in this conference is on Algorithms for GPU, Large-Scale applications, numerical Algorithms and Performance Tuning. The topics include: A communication optimization scheme for basis computation of krylov subspace methods on multi-GPUs;heterogenous acceleration for linear algebra in multi-coprocessor environments;a study of SpMV implementation using MPI and OpenMP on Intel many-core architecture;SIMD implementation of a multiplicative Schwarz smoother for a multigrid Poisson solver on an Intel Xeon phi coprocessor;performance optimization of the 3D FDM simulation of seismic wave propagation on the Intel Xeon phi coprocessor using the ppOpen-APPL/FDM library;machine-learning-based load balancing for community ice code component in CESM;domain decomposition for heterojunction problems in semiconductors;a hybrid approach for parallel transistor-level full-chip circuit simulation;self-adaptive multiprecision preconditioners on multicore and manycore architectures;using random butterfly transformations to avoid pivoting in sparse direct methods;hybrid sparse linear solutions with substituted factorization;modeling 1D distributed-memory dense kernels for an asynchronous multifrontal sparse solver;accelerating computation of eigenvectors in the dense nonsymmetric eigenvalue problem;low byte/flop implementation of iterative solver for sparse matrices derived from stencil computations;environment-sensitive performance tuning for distributed service orchestration;historic learning approach for auto-tuning openACC accelerated scientific applications;toward restarting strategies tuning for a krylov eigenvalue solver and performance analysis of the householder-type parallel tall-skinny QR factorizations toward automatic algorithm selection.

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Evolutionary Global Optimization, Manifolds and applications

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2015年

作者： Hime Aguiar e Oliveira

ISBN: (纸本)9783319264660

This book presents powerful techniques for solving global optimization problems on manifolds by means of evolutionary algorithms, and shows in practice how these techniques can be applied to solve real-world problems. It describes recent findings and well-known key facts in general and differential topology, revisiting them all in the context of application to current optimization problems. Special emphasis is put on game theory problems. Here, these problems are reformulated as constrained global optimization tasks and solved with the help of Fuzzy ASA. In addition, more abstract examples, including minimizations of well-known functions, are also included. Although the Fuzzy ASA approach has been chosen as the main optimizing paradigm, the book suggests that other metaheuristic methods could be used as well. Some of them are introduced, together with their advantages and disadvantages. Readers should possess some knowledge of linear algebra, and of basic concepts of numerical analysis and probability theory. Many necessary definitions and fundamental results are provided, with the formal mathematical requirements limited to a minimum, while the focus is kept firmly on continuous problems. The book offers a valuable resource for students, researchers and practitioners. It is suitable for university courses on optimization and for self-study.

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Research about the special type matrix to proof and solve the method of linear algebra

Research about the special type matrix to proof and solve th...

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IEEE International conference on Networking, Sensing and Control

作者： Yan Lin Li Chien-Yun Dai Department of Electrical Engineering National Taiwan Normal University Taipei Taiwan R.O.C Department of Industrial Education National Taiwan Normal University Taipei Taiwan R.O.C

ISBN: (纸本)9781479980703

“Data century has arrived! Having too many applications to discrete mathematics rather than use continuous mathematics, the method instead of using analog to digital methods. The vector and matrix has become the language which we must speak up.” says the author of the professor named Gibert, S. linear algebra is a branch of mathematics that studies the object is a vector, a vector space (or linear space), and finite-dimensional linear transformation of linear equations. Vector space is an important topic in modern mathematics. linear algebra is widely used in abstract algebra and functional analysis; through analytic geometry, linear algebra to be specific representation. The theory of linear algebra has been generalized to operator theory. Due to the science of nonlinear models can be approximated by the linear models. linear algebra was widely used in the natural sciences, engineering, computer and social science. linear algebra originated in the two-dimensional and three-dimensional Cartesian coordinate system research.

关键词： Symmetric matrices Eigenvalues and eigenfunctions Polynomials Mathematical model Matrices

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Real and Integer Extended Rank Reduction Formulas and Matrix Decompositions: A Review 3rd

Real and Integer Extended Rank Reduction Formulas and Matrix...

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3rd International conference on numerical Analysis and Optimization - theory, methods, applications and Technology Transfer ((NAO)

作者： Mahdavi-Amiri, Nezam Golpar-Raboky, Effat Sharif Univ Technol Fac Math Sci Tehran Iran Univ Qom Dept Math Qom Iran

ISBN: (纸本)9783319176895;9783319176888

We have recently developed an extended rank reducing process for rank reduction of a matrix leading to various matrix decompositions containing the Abaffy-Broyden-Spedicato (ABS) and Wedderburn processes. Notably, the extended process contains both the Wedderburn biconjugation process and the scaled extended ABS class of algorithms. The process provides a general finite iterative approach for constructing factorizations of a matrix and its transpose under a common framework of a general decomposition having various useful structures such as triangular, orthogonal, diagonal, banded and Hessenberg and many others. One main new result is the derivation of an extended rank reducing process for an integer matrix leading to the so-called Smith normal form. For this process, to solve the arising quadratic Diophantine equations, we have proposed two algorithms. Here, we report some numerical results on randomly generated test problems showing a better performance of one algorithm, based on a recent ABS algorithm, in controlling the size of the solution. We also report results obtained by our algorithm on the Smith normal form having a more balanced distribution of the intermediate values as compared to the ones obtained by Maple.

关键词： linear systems Matrix decomposition Wedderburn rank reduction ABS Algorithms Smith normal form Quadratic Diophantine equation

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On optimal frame conditioners

On optimal frame conditioners

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International conference on Sampling theory and applications (SampTA)

作者： Chae A. Clark Kasso A. Okoudjou Department of Mathematics University of Maryland College Park

A (unit norm) frame is scalable if its vectors can be rescaled so as to result into a tight frame. Tight frames can be considered optimally conditioned because the condition number of their frame operators is unity. In this paper we reformulate the scalability problem as a convex optimization question. In particular, we present examples of various formulations of the problem along with numerical results obtained by using our methods on randomly generated frames.

关键词： linear programming Scalability Convex functions linear systems Mathematical programming Testing

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The AMPL Modeling Language: An Aid to Formulating and Solving Optimization Problems 3rd

The AMPL Modeling Language: An Aid to Formulating and Solvin...

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3rd International conference on numerical Analysis and Optimization - theory, methods, applications and Technology Transfer ((NAO)

作者： Gay, David M. AMPL Optimizat Inc 900 Sierra Pl SE Albuquerque NM 87108 USA

ISBN: (纸本)9783319176895;9783319176888

Optimization problems arise in many contexts. Sometimes finding a good formulation takes considerable effort. A modeling language, such as AMPL, facilitates experimenting with formulations and simplifies using suitable solvers to solve the resulting optimization problems. AMPL lets one use notation close to familiar mathematical notation to state variables, objectives, and constraints and the sets and parameters that may be involved. AMPL does some problem transformations and makes relevant problem information available to solvers. The AMPL command language permits computing and displaying information about problem details and solutions returned by solvers. It also lets one modify problem formulations and solve sequences of problems. AMPL addresses both continuous and discrete optimization problems and offers some constraint-programming facilities for the latter. More generally, AMPL permits stating and solving problems with complementarity constraints. For continuous problems, AMPL makes first and second derivatives available via automatic differentiation. The freely available AMPL/solver interface library (ASL) facilitates interfacing with solvers. This paper gives an overview of AMPL and its interaction with solvers and discusses some problem transformations and implementation techniques. It also looks forward to possible enhancements to AMPL.

关键词： Mathematical Programming linear Programming Nonlinear Programming Automatic Differentiation

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Optimally sparse image approximation by adaptive linear splines over anisotropic triangulations

Optimally sparse image approximation by adaptive linear spli...

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International conference on Sampling theory and applications (SampTA)

作者： Armin Iske Laurent Demaret University of Hamburg Hamburg Germany Helmholtz Zentrum München ICB Munich Germany

Anisotropic triangulations provide efficient methods for sparse image representations. In previous work, we have proposed a locally adaptive algorithm for sparse image approximation, adaptive thinning, which relies on linear splines over anisotropic Delaunay triangulations. In this contribution, we address theoretical and practical aspects concerning image approximation by linear splines over anisotropic conformal triangulations. Our discussion includes asymptotically optimal N-term approximations on relevant classes of target functions, such as horizon functions across α Hölder smooth boundaries and regular functions of W α, p regularity, for α > 2/p-1. Moreover, we demonstrate the good performance of our adaptive thinning algorithm by numerical examples and comparisons.

关键词： Splines (mathematics) Tin Least squares approximations Wavelet transforms Image coding

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Revisiting the Nyström method for improved large-scale machine learning

The Journal of Machine Learning Research

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The Journal of Machine Learning Research 2016年第1期17卷

作者： Kevin Murphy Bernhard Schölkopf Alex Gittens Michael W. Mahoney Google MPI for Intelligent Systems International Computer Science Institute and Department of Statistics University of California Berkeley Berkeley CA

We reconsider randomized algorithms for the low-rank approximation of symmetric positive semi-definite (SPSD) matrices such as Laplacian and kernel matrices that arise in data analysis and machine learning applications. Our main results consist of an empirical evaluation of the performance quality and running time of sampling and projection methods on a diverse suite of SPSD matrices. Our results highlight complementary aspects of sampling versus projection methods; they characterize the effects of common data preprocessing steps on the performance of these algorithms; and they point to important differences between uniform sampling and nonuniform sampling methods based on leverage scores. In addition, our empirical results illustrate that existing theory is so weak that it does not provide even a qualitative guide to practice. Thus, we complement our empirical results with a suite of worst-case theoretical bounds for both random sampling and random projection methods. These bounds are qualitatively superior to existing bounds--e.g., improved additive-error bounds for spectral and Frobenius norm error and relative-error bounds for trace norm error--and they point to future directions to make these algorithms useful in even larger-scale machine learning applications.

关键词： Nyström approximation kernel methods low-rank approximation numerical linear algebra randomized algorithms

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linear KernelPCA and K-Means Clustering Using New Estimated Eigenvectors of the Sample Covariance Matrix

Linear KernelPCA and K-Means Clustering Using New Estimated ...

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International conference on Machine Learning and applications (ICMLA)

作者： Nassara Elhadji Ille Gado Edith Grall-Maës Malika Kharouf Universite de Technologie de Troyes Troyes FR University of Technology of Troyes Optimisation and Safety System Charles Delaunay Institute Troyes France

In this article, random matrix theory is used to propose a new K-means clustering algorithm via linear PCA. Our approach is devoted to linear PCA estimation when the number of the features d and the number of samples n go to infinity at the same rate. More precisely, we deal with the problem of building a consistent estimator of the eigenvectors of the covariance data matrix. numerical results, based on the normalized mutual information (NMI) and the final error rate (ER), are provided and support our algorithm, even for a small number of features/samples. We also compare our approach to spectral clustering, K-means and traditional PCA methods.

关键词： Principal component analysis Covariance matrices Eigenvalues and eigenfunctions Matrix decomposition Clustering algorithms Erbium Optimization

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Quantized H[infinity] Static Output Control for linear Systems with Interval-Bounded Additive Controller Coefficient Variations

Quantized H[infinity] Static Output Control for Linear Syste...

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International conference on Artificial Intelligence, Modelling and Simulation (AIMS)

作者： Xianggui Guo Jianliang Wang Fang Liao Tianjin Key Laboratory for Control Theory & Applications in Complicated System Tianjin University of Technology Tianjin China School of Electrical and Electronic Engineering Nanyang Technological University Singapore Singapore Temasek Laboratories National University of Singapore Singapore Singapore

ISBN: (纸本)9781467386760

This paper investigates insensitive H ∞ control problems for linear continuous-time systems with input and measurement quantization via static output feedback (SOF). The designed controllers are insensitive to additive interval-bounded controller coefficient variations and are made up of two parts as linear and nonlinear parts. The former is used to achieve the H ∞ performance against external disturbances, unknown initial states and controller coefficient variations. The latter is used to attenuate the effect of input and measurement quantization simultaneously. It should be mentioned that three novel linear matrix inequality (LMI) conditions by using three different methods without introducing a matrix equality constraint as many existing results are obtained. Finally, a numerical example is presented to show the effectiveness and advantages of the proposed methods.

关键词： Quantization (signal) Symmetric matrices Control systems Uncertainty linear matrix inequalities Additives Artificial intelligence

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