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International conference on Antenna theory and Techniques

作者： M. B. Manuilov A. M. Lerer G. P. Sinyavsky Southern Federal University Rostov on Donu Russia

A novel fast and accurate full-wave approach to the analysis of a wide class of slotted waveguide arrays and finite multi-layer waveguide arrays with dielectric cover is presented. The numerical-analytical solution is based on Galerkin method with weighted Chebyshev and Gegenbauer polynomials as basis functions explicitly accounting for the field asymptotic at the edges. An extremely fast convergence of the method is achieved due to proper basis functions. The other key point of the solution is the computational acceleration of double series and integrals which are the matrix elements of a final system of linear algebraic equations. The results for traveling-wave array with shunt slots for radar applications are considered. A parametric study of waveguide antenna arrays with finite multi-layer dielectric cover is presented, which includes the effect of dielectric cover on impedance matching, array efficiency and directivity.

关键词： Dielectrics Antenna arrays Chebyshev approximation Moment methods Polynomials Waveguide theory Apertures

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GPU Accelerated Lanczos Algorithm with applications

GPU Accelerated Lanczos Algorithm with Applications

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International conference on Advanced Information Networking and applications Workshops (AINAW)

作者： Kiran Kumar Matam Kishore Kothapalli International Institute of Information Technology Hyderabad Hyderabad India

Graphics Processing Units provide a large computational power at a very low price which position them as an ubiquitous accelerator. GPGPU is accelerating general purpose computations using GPU's. GPU's have been used to accelerate many linear algebra routines and numerical methods. Lanczos is an iterative method well suited for finding the extreme eigenvalues and the corresponding eigenvectors of large sparse symmetric matrices. In this paper, we present an implementation of Lanczos Algorithm on GPU using the CUDA programming model and apply it to two important problems : graph bisection using spectral methods, and image segmentation. Our GPU implementation of spectral bisection performs better when compared to both an Intel Math Kernel Library implementation and a Matlab implementation. Our GPU implementation shows a speedup up to 97.3 times over Matlab Implementation and 2.89 times over the Intel Math Kernel Library implementation on a Intel Core i7 920 Processor, which is a quad-core CPU. Similarly, our image segmentation implementation achieves a speed up of 3.27 compared to a multicore CPU based implementation using Intel Math Kernel Library and OpenMP. Through this work, we therefore wish to establish that the GPU may still be a better platform for also highly irregular and computationally intensive applications.

关键词： Graphics processing unit Eigenvalues and eigenfunctions Image segmentation Sparse matrices Kernel Instruction sets Symmetric matrices

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Extremal Combinatorics 2

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丛书名： Texts in Theoretical Computer Science. An EATCS Series

2011年

作者： Stasys Jukna

ISBN: (数字)9783642173646

ISBN: (纸本)9783642173639

This book is a concise, self-contained, up-to-date introduction to extremal combinatorics for nonspecialists. There is a strong emphasis on theorems with particularly elegant and informative proofs, they may be called gems of the theory. The author presents a wide spectrum of the most powerful combinatorial tools together with impressive applications in computer science: methods of extremal set theory, the linear algebra method, the probabilistic method, and fragments of Ramsey theory. No special knowledge in combinatorics or computer science is assumed - the text is self-contained and the proofs can be enjoyed by undergraduate students in mathematics and computer science. Over 300 exercises of varying difficulty, and hints to their solution, complete the text. This second edition has been extended with substantial new material, and has been revised and updated throughout. It offers three new chapters on expander graphs and eigenvalues, the polynomial method and error-correcting codes. Most of the remaining chapters also include new material, such as the Kruskal-Katona theorem on shadows, the Lovasz-Stein theorem on coverings, large cliques in dense graphs without induced 4-cycles, a new lower bounds argument for monotone formulas, Dvir's solution of the finite field Kakeya conjecture, Moser's algorithmic version of the Lovasz Local Lemma, Schoning's algorithm for 3-SAT, the Szemeredi-Trotter theorem on the number of point-line incidences, surprising applications of expander graphs in extremal number theory, and some other new results.

关键词： theory of Computation Number theory Discrete Mathematics in Computer Science Discrete Mathematics Computational Mathematics and numerical Analysis

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Theoretical research on structural equation model based on principle of entropy

Theoretical research on structural equation model based on p...

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International conference on E-Business and E-Government (ICEE)

作者： Fuzhan Ren Baoshan Zhao Huixin Yu Aiping Xu Yongjing Hao Hebei University of Technology Tianjin China

ISBN: (纸本)9781424486915

The theory of entropy is an effective tool to solve the uncertain problems, which has a variety of applications in social and natural sciences. Based on the theory of entropy, the basic concepts and principles of entropy and information entropy, maximum entropy and probabilistic distribution are introduced comprehensively and systematically. The modeling method of structural equation model (SEM) mainly includes the linear structure relations based on the covariance structures (LISREL) and the path method based on partial least square (PLS). These two methods have different requirements for data. LISREL requires observed variables with normal distribution, while PLS has no strict restriction on data. The theory of entropy is used in the modeling research of SEM, and the entropy model with data normal distribution is established by introducing the criterion and constraint condition of maximum entropy, and thus the normal distribution is determined. According to this the modeling method of SEM is determined. Therefore, the modeling idea based on the theory of entropy is a useful exploration for the modeling theory of SEM.

关键词： Entropy Mathematical model numerical analysis Gaussian distribution Probability distribution Data models Thermodynamics

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Low complexity least-squares filter design for the correction of linear time-varying systems

Low complexity least-squares filter design for the correctio...

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European conference on Circuit theory and Design, ECCTD

作者： Michael Soudan Christian Vogel Signal Processing and Speech Communication Laboratory Graz University of Technology Graz Austria Telecommunications Research Center Vienna Vienna Austria

In this paper, a low complexity algorithm for the design of a time-varying correction filter of finite impulse response (FIR) type is presented. Using the obtained filter design to correct a preceding time-varying system, a correction performance in the least-squares sense can be ensured. The adaptation of the filter design requires a moderate computational complexity and is suitable for real-time applications. Thus, a correction of non-periodically time-varying systems can be achieved where design methods, which rely on computationally intensive operations, e.g. numerical integration, can not be applied. At the same time, its application is not limited to weakly time-varying systems as iterative solutions are, which can correct for weakly time-varying behavior by gradually reducing the induced signal error over multiple stages.

关键词： Algorithm design and analysis Time varying systems Complexity theory Prediction algorithms Signal processing algorithms Finite impulse response filter

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Fault detection for linear uncertain systems with sensor faults

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IET CONTROL theory AND applications 2010年第6期4卷 923-935页

作者： Yang, G. -H. Wang, H. Beijing Univ Technol Coll Elect Informat & Control Engn Beijing 100124 Peoples R China Northeastern Univ Minist Educ Key Lab Integrated Automat Proc Ind Coll Informat Sci & Engn Shenyang 110004 Peoples R China

The study paper deals with sensor fault detection problem for a class of linear uncertain systems with bounded disturbances and non-zero constant reference inputs. The sensor faults are modelled as multi-mode, named as fault-free mode and faulty modes. A steady-state-based approach is proposed to detect the sensor faults. The steady-state-based approach can be used to detect lock-in-place sensor faults with arbitrary small magnitudes, which has not been well investigated in the literature. A convergent iterative algorithm based on linear matrix inequalities is given to obtain the solutions. A numerical example is given to illustrate the effectiveness of the proposed methods.

关键词： linear uncertain systems fault diagnosis fault trees numerical analysis Combinatorial mathematics convergent iterative algorithm steady-state-based approach linear systems algebra linear algebra (numerical analysis) sensors lock-in-place sensor faults Interpolation and function approximation (numerical analysis) uncertain systems linear matrix inequalities reliability theory iterative methods Reliability theory Maintenance and reliability Reliability fault detection problem

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numerical solution to linear matrix equation by finite steps iteration

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IET CONTROL theory AND applications 2010年第7期4卷 1245-1253页

作者： Li, Z. -Y. Zhou, B. Wang, Y. Duan, G. -R. Harbin Inst Technol Dept Math Harbin 150001 Peoples R China Harbin Inst Technol Ctr Control Theory & Guidance Technol Harbin 150001 Peoples R China

The matrix equation Sigma(l)(i=1)A(i)XB(i) = C, which contains the well-known Sylvester matrix equation and Lyapunov matrix equation as special cases, has many important applications in control system theory. This study presents an iterative algorithm to solve such linear matrix equation. It is shown that the proposed algorithm converges to the unique solution to the linear matrix equation at finite steps for arbitrary initial condition. Moreover, if the matrix equation is not consistent, the least squares solution can be obtained by alternatively solving a linear matrix equation in the same form, which can also be solved by the proposed iterative algorithm. numerical example shows the effectiveness of the proposed approach.

关键词： numerical solution least squares solution iterative algorithm Sylvester matrix equation finite steps iteration linear algebra (numerical analysis) iterative methods control system theory Lyapunov matrix equation linear matrix equation arbitrary initial condition Interpolation and function approximation (numerical analysis) least squares approximations linear matrix inequalities Lyapunov matrix equations numerical approximation and analysis

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Robustness analysis for a class of linear neutral systems in a critical case

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IET CONTROL theory AND applications 2010年第9期4卷 1807-1816页

作者： Quan, Q. Cai, K. -Y. Beijing Univ Aeronaut & Astronaut Dept Automat Control Natl Key Lab Sci & Technol Holist Control Beijing 100191 Peoples R China

This study pays attention to robust stability of a class of uncertain neutral systems in a critical case, where the spectral radius of the principal neutral term (matrix H in this study) is equal to 1. It is shown that usual methods cannot deal with such systems with uncertainties. Thus, a novel method is developed, whose idea is to examine whether or not an existing stability criterion still holds when the uncertainties are sufficiently small. More specifically, it is to examine whether or not the existing stability criterion in terms of a linear matrix inequality (LMI) still has a solution with the sufficiently small uncertainties. By analysing the structure of the solution, a new robust stability criterion is derived in terms of the existence of solutions to an equation. An application shows the effectiveness of the proposed method by dealing with a problem caused by numerical methods when solving LMIs.

关键词： linear neutral systems robust stability criterion stability Stability in control theory uncertain neutral systems linear matrix inequality linear algebra (numerical analysis) numerical methods uncertain systems linear matrix inequalities

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New stabilisation schemes for discrete delay systems with uncertain non-linear perturbations

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IET CONTROL theory AND applications 2010年第12期4卷 2937-2946页

作者： Mahmoud, M. S. Xia, Y. King Fahd Univ Petr & Minerals Syst Engn Dept Dhahran 31261 Saudi Arabia Beijing Inst Technol Dept Automat Control Beijing 100081 Peoples R China

New H(infinity) controller design schemes are provided for a class of discrete-time systems with uncertain non-linear perturbations. The class includes both systems with time-varying delays and systems without delay. One design scheme is generated by state-feedback and the other scheme is based on proportional-summation-difference (PSD) feedback. An appropriate Lyapunov-Krasovskii functional (LKF) is constructed and a new parametrised characterisation is established in terms of feasibility-testing of linear matrix inequalities (LMIs). numerical examples are given to illustrate the theoretical developments.

关键词： H∞ control nonlinear systems perturbation techniques time-varying systems Time-varying control systems stability control system synthesis Stability in control theory Control system analysis and synthesis methods appropriate Lyapunov-Krasovskii functional Nonlinear control systems state feedback discrete delay systems proportional-summation-difference feedback linear algebra (numerical analysis) Lyapunov methods uncertain nonlinear perturbations H∞ controller design schemes uncertain systems linear matrix inequalities Optimal control Discrete control systems delay systems discrete-time systems time-varying delays Distributed parameter control systems discrete time systems state-feedback stabilisation schemes

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Design of reduced-order l₂-l_∞ filter design for singular discrete-time systems using strict linear matrix inequalities

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IET CONTROL theory AND applications 2010年第3期4卷 509-519页

作者： Mahmoud, M. S. Xia, Y. King Fahd Univ Petr & Minerals Dept Syst Engn Dhahran 31261 Saudi Arabia Beijing Inst Technol Dept Automat Control Beijing 100081 Peoples R China

In this study, the problem of designing regular robust l(2)-l(infinity) filter for a class of linear singular discrete-time systems with norm-bounded uncertainties is investigated. A class of regular linear filters is fully analysed, then necessary and sufficient conditions of robust admissibility are established. Guaranteed l(2)-l(infinity) performance of the filtered system is provided and expressed in terms of the solution of strict linear matrix inequalities (LMIs). The cases of full- and zeroth-order realisable filter are derived as limiting cases of design. numerical examples are worked out to illustrate the theoretical development.

关键词： Signal processing theory filtering theory linear algebra (numerical analysis) strict linear matrix inequality l∞ filter design reduced order l2 filter linear singular discrete time systems norm bounded uncertainties discrete time systems Filtering methods in signal processing linear matrix inequalities zeroth order filter

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