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numerical linear algebra FOR NONlinear MICROWAVE IMAGING

ELECTRONIC TRANSACTIONS ON numerical ANALYSIS 2008年 33卷 105-125页

作者： Di Benedetto, Fabio Estatico, Claudio Nagy, James G. Pastorino, Matteo Univ Genoa Dipartimento Matemat I-16146 Genoa Italy Univ Cagliari Dipartimento Matemat & Informat I-09124 Cagliari Italy Emory Univ Dept Math & Comp Sci Atlanta GA 30322 USA Univ Genoa Dipartimento Ingn Biofis & Elettron I-16145 Genoa Italy

A nonlinear inverse scattering problem arising in microwave imaging is analyzed and numerically solved. In particular, the dielectric properties of an inhomogeneous object (i.e., the image to restore) are retrieved by means of its scattered microwave electromagnetic field (i.e., the input data) in a tomographic arrangement. From a theoretical point of view, the model gives rise to a nonlinear integral equation, which is solved by a deterministic and regularizing inexact Gauss-Newton method. At each step of the method, matrix strategies of numerical linear algebra are considered in order to reduce the computational (time and memory) load for solving the obtained large and structured linear systems. These strategies involve block decompositions, splitting and regularization, and super-resolution techniques. Some numerical results are given where the proposed algorithm is applied to recover high resolution images of the scatterers.

关键词： inverse scattering microwave imaging inexact-Newton methods block decomposition regularization

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Convergence conditions for splitting iteration methods for non-Hermitian linear systems

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linear algebra AND ITS applications 2008年第2-3期428卷 453-468页

作者： Wang, Li Bai, Zhong-Zhi Chinese Acad Sci Acad Math & Syst Sci Inst Computat Math & Sci Engn Comp State Key Lab Sci Engn Comp Beijing 100080 Peoples R China Nanjing Normal Univ Sch Math & Comp Sci Dept Computat Math Nanjing Peoples R China

Necessary and sufficient convergence conditions are studied for splitting iteration methods for non-Hermitian system of linear equations when the coefficient matrix is non-singular. When this theory is specialized to the generalized saddle-point problem, we obtain convergence theorem for a class of modified accelerated overrelaxation iteration methods, which include the Uzawa and the inexact Uzawa methods as special cases. Moreover, we apply this theory to the two-stage iteration methods for non-Hermitian positive definite linear systems, and obtain sufficient conditions for guaranteeing the convergence of these methods. (c) 2007 Elsevier Inc. All rights reserved.

关键词： non-Hermitian linear systems splitting iteration method convergence

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Matrix-Based Multigrid 2nd ed. 2008

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丛书名： numerical methods and Algorithms

2008年

作者： Yair Shapira

ISBN: (数字)9780387497655

ISBN: (纸本)9780387497648

This book introduces and analyzes the multigrid approach for the numerical solution of large sparse linear systems arising from the discretization of elliptic partial differential equations. Special attention is given to the powerful matrix-based-multigrid approach, which is particularly useful for problems with variable coefficients and nonsymmetric and indefinite problems. This approach applies not only to model problems on rectangular grids but also to more realistic applications with complicated grids and domains and discontinuous coefficients. Matrix-Based Multigrid can be used as a textbook in courses in numerical analysis, numerical linear algebra, and numerical PDEs at the advanced undergraduate and graduate levels in computer science, math, and applied math departments. The theory is written in simple algebraic terms and therefore requires preliminary knowledge in basic linear algebra and calculus only. Because it is self contained and includes useful exercises, the book is also suitable for self study by research students, researchers, engineers, and others interested in the numerical solution of partial differential equations.

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A fast full multigrid solver for applications in image processing

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numerical linear algebra WITH applications 2008年第2-3期15卷 187-200页

作者： Stuermer, M. Koestler, H. Ruede, U. Univ Erlangen Nurnberg Dept Comp Sci D-91058 Erlangen Germany

We present a fast, cell-centered multigrid solver and apply it to image denoising and non-rigid diffusion-based image registration. In both applications, real-time performance is required in 3D and the multigrid method has to be compared with solvers based on fast Fourier transform (FFT). The optimization of the underlying variational approach results for image denoising directly in one time step of a parabolic linear heat equation, for image registration a non-linear second-order system of partial differential equations is obtained. This system is solved by a fixpoint iteration using a semi-implicit time discretization, where each time step again results in an elliptic linear heat equation. The multigrid implementation comes close to real-time performance for medium size medical images in 3D for both applications and is compared with a solver based on FFT using available libraries. Copyright (c) 2007 John Wiley & Sons, Ltd.

关键词： multigrid performance optimization FFT image processing image registration image denoising

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linear algebra: Ideas and applications

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2008年

作者： Richard C Penney

ISBN: (纸本)9780470178843

This expanded new edition presents a thorough and up-to-date introduction to the study of linear algebra linear algebra, Third Edition provides a unified introduction to linear algebra while reinforcing and emphasizing a conceptual and hands-on understanding of the essential ideas. Promoting the development of intuition rather than the simple application of methods, the book successfully helps readers to understand not only how to implement a technique, but why its use is important. The book outlines an analytical, algebraic, and geometric discussion of the provided definitions, theorems, and proofs. For each concept, an abstract foundation is presented together with its computational output, and this parallel structure clearly and immediately illustrates the relationship between the theory and its appropriate applications. The Third Edition also features: * A new chapter on generalized eigenvectors and chain bases with coverage of the Jordan form and the Cayley-Hamilton theorem * A new chapter on numerical techniques, including a discussion of the condition number * A new section on Hermitian symmetric and unitary matrices * An exploration of computational approaches to finding eigenvalues, such as the forward iteration, reverse iteration, and the QR method * Additional exercises that consist of application, numerical, and conceptual questions as well as true-false questions Illuminating applications of linear algebra are provided throughout most parts of the book along with self-study questions that allow the reader to replicate the treatments independently of the book. Each chapter concludes with a summary of key points, and most topics are accompanied by a "Computer Projects" section, which contains worked-out exercises that utilize the most up-to-date version of MATLAB(r). A related Web site features Maple translations of these exercises as well as additional supplemental material. linear algebra, Third Edition is an excellent undergraduate-level textbook for c

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A Bayesian approach to 3D object recognition using linear combination of 2D views

A Bayesian approach to 3D object recognition using linear co...

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3rd International conference on Computer Vision theory and applications

作者： Zografos, Vasileios Buxton, Bernard F. UCL Dept Comp Sci London WC1E 6BT England

ISBN: (纸本)9789898111210

We introduce Bayes priors into a recent pixel-based, linear combination of views object recognition technique. Novel views of an object are synthesized and matched to the target scene image using numerical optimisation. Experiments on a real-image, public database with the use of two different optimisation methods indicate that the priors effectively regularize the error surface and lead to good performance in both cases. Further exploration of the parameter space has been carried out using Markov Chain Monte Carlo sampling.

关键词： object recognition linear combination of views Bayes Markov-Chain Monte-Carlo

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Computational Approach to Essential and Nonessential Objective Functions in linear Multicriteria Optimization

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JOURNAL OF OPTIMIZATION theory AND applications 2008年第3期139卷 577-590页

作者： Malinowska, A. B. Torres, D. F. M. Bialystok Tech Univ Fac Comp Sci Bialystok Poland Univ Aveiro Dept Math P-3800 Aveiro Portugal

The question of obtaining well-defined criteria for multiple-criteria decision making problems is well known. One of the approaches dealing with this question is the concept of nonessential objective functions. A certain objective function is called nonessential if the set of efficient solutions is the same with or without that objective function. We present two methods for determining nonessential objective functions. A computational implementation is done using a computer algebra system.

关键词： Multiobjective optimization problems Efficient (Pareto optimal) solutions Essential nonessential objective functions

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Non-causal Fliess operators and their shuffle algebra

Non-causal Fliess operators and their shuffle algebra

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Workshop in Honor of the 60th Birthday of Michael Fliess

作者： Gray, W. S. Wang, Y. Old Dominion Univ Dept Comp Sci Norfolk VA 23529 USA Florida Atlantic Univ Dept Math Sci Boca Raton FL 33431 USA

Fliess operators as a class of non-linear operators have been well studied in several respects. They have a well developed realization theory and convenient representations in terms of directed infinite products of exponential Lie series. Their interconnection as subsystems has been studied, as has their relationship to rational systems. They find applications in such diverse areas as discretization methods for controls systems, optimal control, neural network analysis, and the numerical solution of stochastic differential equations. One issue concerning Fliess operators, however, that has received little attention is their possible generalization to the non-causal case. Examples of such operators appear implicitly in the literature addressing Hilbert adjoints of causal non-linear operators and system inversion for the purpose of output tracking. But a general, systematic treatment of the subject has not appeared. In this paper, a non-causal extension of a Fliess operator is developed with the primary focus being on local convergence, continuity, the associated shuffle algebra, and computing adjoint operators.

关键词： algebra

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A parallel approach for a block tri-diagonal solver in fusion simulation

A parallel approach for a block tri-diagonal solver in fusio...

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2008 International conference on Parallel and Distributed Processing Techniques and applications, PDPTA 2008

作者： Yang, Huiqing H. Sanchez, Raul Lynch, Vickie Fusion, Steven Hirshman Department of Math and Computer Science Virginia State University Petersburg VA 23806 United States Energy Division Oak Ridge National Laboratory Oak Ridge TN United States

ISBN: (纸本)1601320841

Simulations of fusion experiments provide important support for fusion experiments. Up to date, the study of fusion experiments has been focused on numerical methods by means of computing power. However, the accurate numerical method has always been a major issue. Based on a Scalable Island Equilibrium Solver for Toroidal Application (SIESTA), an algorithm for solving a huge tri- diagonal system is introduced in this paper. The main effort of the paper is placed on studying the computation of a huge tri-diagonal matrix in parallel. A parallel approach is investigated, in which a mapping is defined. The approach guarantees each different matrix block is associated with a unique processor. By means of Basic linear algebra Communication Subprograms (BLACS) and Message Passing Interface (MPI), the parallel approach is implemented on the Jaguar supercomputer. The numerical results and efficiency analysis are provided.

关键词： numerical methods

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Simulate the State Changing of a Descriptor System in (Almost) Zero Time Using the Normal Probability Distribution

Simulate the State Changing of a Descriptor System in (Almos...

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International conference on Computer Modeling and Simulation, UKSIM

作者： Grigoris I. Kalogeropoulos Athanasios A. Karageorgos Athanasios A. Pantelous Department of Mathematics University of Athens (NKUA) Greece School of Engineering and Mathematical Sciences City University UK

In number of control applications, the ability of manipulate the state vector from the input is more than vital. Thus, in the present paper, we develop analytically a methodology for the state changing of a linear control descriptor differential system based also on a linear combination of Dirac δ-function and its derivatives. Using linear algebra techniques and the generalized inverse theory, the input’s coefficients are determined. In our practical numerical application, the Dirac distribution is approximated by the normal probability distribution.

关键词： Probability distribution Vectors Computational modeling Computer simulation Distributed computing Mathematical model Mathematics Control systems linear algebra Control system synthesis

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