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9th International conference on numerical methods and Computational Mechanics (NMCM2002)

作者： Giraud, L Langou, J Rozloznik, M CERFACS F-31057 Toulouse France Acad Sci Czech Republ Inst Comp Sci CZ-18207 Prague Czech Republic Tech Univ Liberec CZ-18207 Prague Czech Republic

In this paper, we study numerical behavior of several computational variants of the Gram-Schmidt orthogonalization process. We focus on the orthogonality of computed vectors which may be significantly lost in the classical or modified Gram-Schmidt algorithm, while the Gram-Schmidt algorithm with reorthogonalization has been shown to compute vectors which are orthogonal to machine precision level. The implications for practical implementation and its impact on the efficiency in the parallel computer environment are considered. (c) 2005 Elsevier Ltd. All rights reserved.

关键词： numerical linear algebra QR factorization Gram-Schmidt orthogonalization reorthogonalization rounding error analysis

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Random matrix methods for design of multiuser communication systems

Random matrix methods for design of multiuser communication ...

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conference on applications of Random Matrices to Economy and Other Complex Systems

作者： Müller, Ralf R. Norwegian University of Science and Technology N-7491 Trondheim Norway

A short review on multiuser communication systems is given. System design for iterative multiuser decoding is improved by means of large system results from statistical physics and random matrix theory. With the application of multiuser detection for wireless communications in mind, it is shown how a system of linear equations with random coefficients can be solved efficiently exploiting the asymptotic convergence of its eigenvalue spectrum. In addition, the conditional convergence of the diagonal elements of a power of a random matrix drawn from a Marchenko-Pastur ensemble is established.

关键词： Matrix algebra

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Performance Evaluation of Sparse Storage Formats

Performance Evaluation of Sparse Storage Formats

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International conference on Information and Communication Technologies (ICICT)

作者： A. Usman M. Lujan L. Freeman Pakistan Institute of Engineering and Applied Sciences Islamabad Pakistan Centre for Novel Computing University of Manchester Institute of Science and Technology Manchester UK

Sparse matrices are pervasive in many Computational Science and Engineering (CS&E) applications. There is a significant number of storage formats used to represent sparse matrices. This paper presents a performance evaluation of storage formats for the main kernel of iterative methods for numerical linear algebra, namely matrix-vector multiplication. The experiments consider a set of almost 200 sparse matrices from the Matrix Market collection covering both systems of linear equations and eigenvalue problems. For each matrix, the experiments perform the matrix-vector multiplication with most commonly used sparse storage formats and also the recently proposed Java Sparse Array storage fonmat. To the best of the authors' knowledge, there is no other performance evaluation of storage formats for sparse matrices which consider such a variety of matrices and storage formats.

关键词： Sparse matrices Pervasive computing Kernel Iterative methods linear algebra Equations Eigenvalues and eigenfunctions Java

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Synthesis of Beam Lines with Necessary Properties

Synthesis of Beam Lines with Necessary Properties

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IEEE conference on Particle Accelerator

作者： S.N. Andrianov Saint Petersburg State Polytechnical University Saint Petersburg Russia

In this paper a new approach to the problem of synthesis of beam lines is discussed. Usually this problem can be overcome by the use of numerical simulation and opti mal control theory methods. But this results in sufficiently great number of variable parameters and functions. Obviously, that this degrades quality of a modeling procedure. The suggested approach is demonstrated on a problem of a microprobe design problem. Essence of the problem is that necessary to design a high precision focusing system which satisfies some additional conditions. For solution of this problem we use an algebraic treatment based on Lie algebraic methods and computer algebra techniques. Using the symmetry ideology this approach allows rewriting beam properties to enough simple conditions for control parameters and functions. This leads a set of desired solutions and show results in some most suitable form. Moreover, this approach decreases the number of variable parameters.

关键词： Focusing Optimal control Optical beams numerical simulation Degradation algebra Process design Particle beams linear approximation Length measurement

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A tubular linear motor for micro robotic applications

A tubular linear motor for micro robotic applications

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International conference on Mechatronics (ICM)

作者： Haiwei Lu Jianguo Zhu Youguang Guo Faculty of Engineering University of Technology Sydney Australia

linear micro motors play a key role in micro robotic systems. They can greatly simplify the drive mechanisms, which is crucial for micro systems. By using permanent magnets, much higher force-to-volume ratios can be acquired than using electromagnets and better drive performance can be obtained. This paper describes the development of a tubular permanent magnet linear motor for the actuation of micro robots. Important design criteria are established by both analytical and numerical methods. The performances of the micro motor as well as the entire actuation system are analyzed and predicted by the finite element analysis and kinetic modeling. The results show that the proposed linear motor has the quite satisfactory force capability and kinetic performance.

关键词： Micromotors Robots Magnetic analysis Permanent magnet motors Performance analysis Kinetic theory Permanent magnets Electromagnets Finite element methods Predictive models

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numerical Modeling and Inverse Scattering in Nondestructive Testing: Recent applications and Advances

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AIP conference Proceedings 2005年第1期760卷 775-782页

作者： R. Marklein K. J. Langenberg K. Mayer A. Shlivinski J. Miao A. Zimmer W. Müller V. Schmitz C. Kohl U. Mletzko 1Electromagnetic Theory Department of Electrical Engineering and Computer Science University of Kassel D‐34109 Kassel Germany 2Fraunhofer Institute for Nondestructive Testing (IZFP) University Building 37 D‐66123 Saarbrücken Germany 3Federal Research Institute for Material Research and Testing D‐12200 Berlin Germany 4MPA/NDT Group University of Stuttgart D‐70511 Stuttgart Germany

This paper presents recent advances and future challenges of the application of different numerical modeling tools and linear and nonlinear inversion algorithms in ultrasonics and electromagnetics applied in NDE. The inversion methods considered in the presented work vary from linear schemes, e.g. SAFT/InASAFT and Diffraction Tomography/FT‐SAFT, to nonlinear schemes, e.g. the Contrast Source Inversion. Inversion results are presented and compared for modeled and measured ultrasonic and electromagnetic data to locate voids and cracks as well as to locate aluminum tendon ducts in concrete, which is a typical GPR problem. Finite Integration Technique (FIT) and Domain Integral Equation (DIE) solvers are used as modeling tools.

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Application of digital control theory to exact discretization of a logistic equation with a constant term

Application of digital control theory to exact discretizatio...

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IEEE conference on Control Technology and applications (CCTA)

作者： N. Hori C.A. Rabbath Digital Control Laboratory Graduate School of Systems and Information Engineering University of Tsukuba Tsukuba Ibaraki Japan Defence Research and Development Canada Val-Belair QUE Canada

This paper presents an exact method of discretizing a logistic differential equation with a constant term (a class of Riccati equation), which are prevalent in a variety of fields, using a common knowledge in digital control theory. The resulting model gives the value that is exact at the discrete-time instants for any discretization period. Two existing methods that can lead to an exact discrete-time model are second-order and shown to be based on diverging variables, while the one proposed in this study is first-order and not prone to such a numerical problem. A simulation result is presented to illustrate this issue

关键词： Digital control Logistics Riccati equations Nonlinear systems Differential equations Nonlinear equations Chaos linear systems Nonlinear control systems Sampling methods

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On solving periodic differential matrix equations with applications to periodic system norms computation

On solving periodic differential matrix equations with appli...

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IEEE conference on Decision and Control

作者： A. Varga German Aerospace Center DLR-Oberpfaffenhofen Institute of Robotics and Mechatronics Wessling Germany

ISBN: (纸本)0780395670

Periodic Lyapunov, Sylvester and Riccati differential equations have many important applications in the analysis and design of linear periodic control systems. For the numerical solution of these equations efficient numerically reliable algorithms based on the periodic Schur decomposition are proposed. The new multi-shot type algorithms compute periodic solutions in an arbitrary number of time moments within one period by employing suitable discretizations of the continuous-time problems. In contrast to traditionally used one-shot periodic generator methods, the multi-shot type methods have the advantage to be able to address problems with large periods and/or unstable dynamics. applications of the proposed techniques to compute several system norms are presented.

关键词： Differential equations Riccati equations Control systems Aerodynamics Eigenvalues and eigenfunctions Control system analysis Controllability Observability Filtering theory Software algorithms

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Resultant Based methods Computing the Greatest Common Divisor of Several Polynomials

Resultant Based Methods Computing the Greatest Common Diviso...

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IEEE International Symposium on Intelligent Control (ISIC)

作者： D. Triantafyllou M. Mitrouli N. Karcanias Department of Mathematics University of Athens (NKUA) Athens Greece Control Engineering Centre School of Engineering and Mathematical Science City University Northampton Square London UK

In this paper we develop two resultant based methods for the computation of the greatest common divisor (GCD) of many polynomials. Let S be the resultant Sylvester's matrix of the polynomials. The application of classical LU and QR factorization to S for the computation of its GCD has an inappropriate complexity of order O(n 4 ). We modified matrix S to S* such that the rows with non-zero elements under the main diagonal, at every column, are gathered together. We constructed modified versions of the LU and QR procedures which lead to the computation of the GCD of S* in O(n 3 ) floating point operations. Both methods are tested for several sets of polynomials and tables summarizing all the achieved results are given

关键词： Polynomials Computer errors Testing numerical analysis linear algebra Control theory Matrices Statistical analysis Floating-point arithmetic Stability

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On the positivity of matrix-vector products

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linear algebra AND ITS applications 2004年第1-3期393卷 253-258页

作者： Horváth, Z Szechenyi Istvan Univ Dept Math H-9026 Gyor Hungary

In this paper we examine the positivity of Rv where R is an element of R-NxN, v is an element of R-N, v greater than or equal to 0 with R = r(tauA), r is a given (rational) function, A is an element of R-NxN and tau is an element of (0, infinity). Here we mean by positivity the ordering w.r.t. an arbitrary order cone, which includes the classical entrywise positivity of vectors. Since the requirement R greater than or equal to 0 leads to very severe restrictions on r and tau we construct apositive cone P = P(A) and determine tau* = tau*(r, P) such that r(tauA)P subset of P for all tau is an element of [0, tau*]. Finally we give an example arising from applications to partial differential equations where our results explain actual computations much better than the general theory on R greater than or equal to 0. (C) 2004 Elsevier Inc. All rights reserved.

关键词： positive matrices invariant cone positivity numerical methods

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