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Meromorphic functions and linear algebra

丛书名： Fields Institute monographs,

2003年

作者： Olavi Nevanlinna

ISBN: (数字)9781470431457

ISBN: (纸本)9780821832479

This volume describes for the first time in monograph form important applications in numerical methods of linear algebra. The author presents new material and extended results from recent papers in a very readable style. The main goal of the book is to study the behavior of the resolvent of a matrix under the perturbation by low rank matrices. Whereas the eigenvalues (the poles of the resolvent) and the pseudospectra (the sets where the resolvent takes large values) can move dramatically under such perturbations, the growth of the resolvent as a matrix-valued meromorphic function remains essentially unchanged. This has practical implications to the analysis of iterative solvers for large systems of linear algebraic equations. First, the book introduces the basics of value distribution theory of meromorphic scalar functions. It then introduces a new nonlinear tool for linear algebra, the total logarithmic size of a matrix, which allows for a nontrivial generalization of Rolf Nevanlinna's characteristic function from the scalar theory to matrix- and operator-valued functions. In particular, the theory of perturbations by low rank matrices becomes possible. As an example, if the spectrum of a normal matrix collapses under a low rank perturbation, there is always a compensation in terms of the loss of orthogonality of the eigenvectors. This qualitative phenomenon is made quantitative by using the new tool. applications are given to rational approximation, to the Kreiss matrix theorem, and to convergence of Krylov solvers. The book is intended for researchers in mathematics in general and especially for those working in numerical linear algebra. Much of the book is understandable if the reader has a good background in linear algebra and a first course in complex analysis.

关键词： algebra Mathematical Analysis - Complex Analysis

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Solving linear initial value problems by Faber polynomials

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numerical linear algebra WITH applications 2003年第3期10卷 247-270页

作者： Novati, P Univ Trieste Dipartimento Sci Matemat I-34100 Trieste Italy

In this paper we use the theory of Faber polynomials for solving N-dimensional linear initial value problems. In particular, we use Faber polynomials to approximate the evolution operator creating the so-called exponential integrators. We also provide a consistence and convergence analysis. Some tests where we compare our methods with some Krylov exponential integrators are finally shown. Copyright (C) 2002 John Wiley Sons, Ltd.

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Automated symbolic generation of vector graph theoretic object based non-linear dynamic simulation models

Automated symbolic generation of vector graph theoretic obje...

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2003 Summer Computer Simulation conference, SCSC 2003

作者： Sarathy, Sriprakash P. Shujaee, Khalil A. Canon, Kayin R. Clark Atlanta University AtlantaGA30314 United States Georgia Institute of Technology AtlantaGA30332 United States

ISBN: (纸本)1565552687

Developing a comprehensive simulation model of a multi- body system (MBS) is not a trivial task, however, over the years many tools and techniques have been developed to make this task easy and less cumbersome. Many of the innovations and advances have come in three areas;(i)modeling interface, (ii)efficient numerical formulations, and (iii)enhanced computational schemes. With the advent of powerful computational capabilities, the emphasis has shifted away from modeling innovation, to enhanced computational approaches. The ability to turn a model on its head and examine it form an analytical perspective, has yielded to powerful visualization tools that make sense of reams of numerical data generated by complex codes. Yet, the essential role of a simulation model, namely to provide a manageable representation of reality that can be useful in comprehending the phenomena, has not changed one iota. Presented here is a generic, unified. topologically based approach, which uses a minimal set of generalized coordinates, and a minimal set of constraint equations to completely model physical systems of significant complexity. The core formulation is based on well known graph theoretic methods, popular in linear network theory, and controller design theory, among other fields. The present formulation is built on the dual vector approach for dynamics championed by Andrew. Kesavan, and others. Later work (Baciu. McPhee) showed its applicability for dynamical analyses of multi-body systems (MBS). The authors have married this approach with a object oriented physically based modeling technique to enhance its usability and universal applicability. This paper outlines the characteristics of such an approach, through an actual implementation of a MBS closely integrated with a controller, with respect to real time nonlinear simulation applications.

关键词： Graph theory

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Implementation and evaluation of SDPA 6.0 (SemiDefinite Programming algorithm 6.0)

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OPTIMIZATION methods & SOFTWARE 2003年第4期18卷 491-505页

作者： Yamashita, M Fujisawa, K Kojima, M Tokyo Inst Technol Grad Sch Informat Sci & Engn Tokyo 1528552 Japan Tokyo Denki Univ Dept Math Sci Hatoyama Saitama 3500394 Japan

SDP (SemiDefinite Programming) is one of the most attractive optimization models. It has many applications from various fields such as control theory, combinatorial and robust optimization, and quantum chemistry. The SDPA (SemiDefinite Programming Algorithm) is a software package for solving general SDPs based on primal-dual interior-point methods with the HRVW/KSH/M search direction. It is written in C++ with the help of LAPACK for numerical linear algebra for dense matrix computation. The purpose of this paper is to present a brief description of the latest version of the SDPA and its high performance for large scale problems through numerical experiments and comparisons with some other major software packages for general SDPs.

关键词： SemiDefinite Program interior-point method optimization software numerical experiment

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Concise numerical mathematics /

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2003年

作者： Plato Robert

来源：内蒙古大学图书馆图书评论

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numerical solution of large non-Hermitian eigenvalue problem arising from model of vertical cavity surface emitting laser array

Numerical solution of large non-Hermitian eigenvalue problem...

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5th International conference on numerical methods and applications, NMA 2002

作者： Elkin, Nikolay N. Troitsk Moscow Region142190 Russia

ISBN: (纸本)3540006087

Modal behavior of a 2-D (square lattice geometry) antiguided vertical cavity surface emitting laser (VCSEL) array was studied numerically. The background of the numerical model of VCSEL array is scalar diffraction theory and 3-D bidirectional beam propagation method. Resonator modes were found as eigen-functions of the socalled round-trip operator which transforms the transverse distribution of electro-magnetic field when light have a round-trip in the device. The round-trip operator after corresponding discretization becomes a linear non-hermitian operator in a complex linear large dimensional space. Using the Arnoldi algorithm, a number of array optical modes were found. In calculations, both Fourier and space variable descriptions of beam propagation were combined. Calculations were made for various spacing length between elements and a size of the array. 4x4 and 10x10 laser arrays were studied numerically. Array optical modes having different symmetry properties were found. They include in-phase mode with constant phase over the array, out-of-phase mode with alternating phase between elements and modes with mixed symmetry. Conditions are found for favorable lasing of the in-phase mode providing high laser beam quality. © Springer-Verlag Berlin Heidelberg 2003.

关键词： numerical models

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International conference on Computational Science, ICCS 2003

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International conference on Computational Science, ICCS 2003

ISBN: (纸本)9783540401957

The proceedings contain 119 papers. The special focus in this conference is on Computational Finance, Economics, numerical methods for Structured Systems and High Performance Environmental Computations. The topics include: Parallel computing method of valuing for multi-asset European option;a fuzzy approach to portfolio rebalancing with transaction costs;mining investment venture rules from insurance data based on decision tree;double auction in two-level markets;a set of data mining models to classify credit cardholder behavior;continuous time Markov decision processes with expected discounted total rewards;model on analysis of industrial relation based on the binary relation theory;multi-symplectic spectral methods for the sine-Gordon equation;a discrete approach for the inverse singular value problem in some quadratic group;a symplectic lanczos-type algorithm to compute the eigenvalues of positive definite Hamiltonian matrices;applying stabilization techniques to orthogonal gradient flows;coupling general circulation models on a meta-computer;optimal numerical realization of the energy balance equation for wind wave models;simulation of water exchange in enclosed water bodies;a baroclinic three dimensional numerical model applied to coastal lagoons;stochastic simulation of inhomogeneous metocean fields;performance comparison of process allocation schemes depending upon resource availability on grid computing environment;efficient load balancing by adaptive bypasses for the migration on the internet;generalization of the fast consistency algorithm to a grid with multiple high demand zones and linear algebra computation benchmarks on a model grid platform.

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Perturbation theory for matrix equations /

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2003年

作者： Mihail Konstantinov ... [et al.].

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Robust output tracking control of a linear brushless DC motor with time-varying disturbances

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IEE PROCEEDINGS-ELECTRIC POWER applications 2002年第1期149卷 39-45页

作者： Shieh, NC Tung, PC Lin, CL Natl Cent Univ Dept Mech Engn Chungli 32054 Taiwan Feng Chia Univ Dept Automat Control Engn Taichung 40724 Taiwan

Robust output tracking control of a linear brushless DC motor for transportation within a manufacturing system is presented. System identification for a linear motor with a driver is performed by a dynamic signal analyser, thus providing a linearised model for the motor. External disturbances corrupting the driver and modelling uncertainties due to payload variations and identification errors are considered. A tracking control scheme with a guaranteed H, tracking performance is proposed. It is shown that a state feedback control law achieving the desired objective can be obtained by solving a Riccati matrix equation. Computer simulation and experimental implementation are completed and compared. These results demonstrate the effectiveness of the proposed scheme for output tracking control of the linear brushless DC motor, and also confirm the feasibility of its implementation in industrial applications.

关键词： electric machine analysis computing linear motors dynamic signal analyser payload variations system identification Power engineering computing machine theory Riccati equations linear algebra (numerical analysis) H∞ control manufacturing system Optimal control control performance control simulation control design linear brushless DC motor time-varying disturbances transportation industrial applications control system synthesis Riccati matrix equation machine control H∞ tracking performance Control system design and analysis linear machines tracking Control system analysis and synthesis methods computer simulation numerical analysis robust output tracking control Control of electric power systems brushless DC motors d.c. machines robust control identification errors Stability in control theory control system analysis computing modelling uncertainties

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Computing a robust D-stability bound using a parameter-dependent Lyapunov approach

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IEE PROCEEDINGS-CONTROL theory AND applications 2002年第6期149卷 505-510页

作者： Bachelier, O Peaucelle, D Arzelier, D ESIP LAII F-86022 Poitiers France CNRS LAAS F-31077 Toulouse 4 France

The problem of robust matrix root-clustering against additive structured uncertainty is addressed. A bound on the size of the uncertainty domain preserving matrix D-stability is derived from an LMI approach. A recently proposed sufficient condition for robust matrix D-stability with respect to convex polytopic uncertainty is used. It is relevant to the framework dealing with parameter-dependent Lyapunov functions. Using this condition, the problem of computing the robustness bound is formulated as a generalised eigenvalue problem, that enables the bound value to be maximised.

关键词： robustness bound LMI approach feedback linear matrix inequalities control system analysis linear algebra (numerical analysis) robust D-stability bound sufficient condition stability convex polytopic uncertainty eigenvalues and eigenfunctions matrix D-stability additive structured uncertainty robust matrix root-clustering parameter-dependent Lyapunov approach Control system analysis and synthesis methods generalised eigenvalue problem robust control Stability in control theory

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