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International conference on Recent Advances in Microwave theory and applications, MICROWAVE

作者： Manidipa Bhattacharya B Gupta SAMEER Kolkata India Department of Electronics and Telecommunication Engineering Jadavpur University Kolkata India

Artificial neural networks (ANN) are popular as efficient alternatives to conventional computational models like numerical modeling or analytical methods for RF and Microwave modeling and design[1]. Such models reduce both processing time and analytical complexity resulting in simpler computation process. Thus the technique has greater potential in the analysis of various problems in electromagnetism. In the present problem neural network technique has been used for non-linear modeling of the frequency response of the scattering properties of a circular dielectric cylinder in a three dimensional rectangular waveguide at X band. The scattering properties of the vertical posts are analyzed by semi analytical approach based on image theory and the scattered fields are calculated from the lattice sum and the transition matrices. Analysis results have been used to generate S parameter data for the configuration in order to train the proposed network.

关键词： Neural networks Scattering parameters Dielectrics Rectangular waveguides Artificial neural networks numerical models Image analysis Computer networks Computational modeling Analytical models

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linear system solution by null-space approximation and projection (SNAP)

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numerical linear algebra WITH applications 2007年第1期14卷 61-82页

作者： Ilic, M. Turner, I. W. Saad, Y. Queensland Univ Technol Sch Math Sci St Lucia Qld Australia Univ Minnesota Dept Comp Sci & Engn Minneapolis MN 55455 USA

Solutions of large sparse linear systems of equations are usually obtained iteratively by constructing a smaller dimensional subspace such as a Krylov subspace. The convergence of these methods is sometimes hampered by the presence of small eigenvalues, in which case, some form of deflation can help improve convergence. The method presented in this paper enables the solution to be approximated by focusing the attention directly on the 'small' eigenspace ('singular vector' space). It is based on embedding the solution of the linear system within the eigenvalue problem (singular value problem) in order to facilitate the direct use of methods such as implicitly restarted Arnoldi or Jacobi-Davidson for the linear system solution. The proposed method, called 'solution by null-space approximation and projection' (SNAP), differs from other similar approaches in that it converts the non-homogeneous system into a homogeneous one by constructing an annihilator of the right-hand side. The solution then lies in the null space of the resulting matrix. We examine the construction of a sequence of approximate null spaces using a Jacobi-Davidson style singular value decomposition method, called restarted SNAP-JD, from which an approximate solution can be obtained. Relevant theory is discussed and the method is illustrated by numerical examples where SNAP is compared with both GMRES and GMRES-IR. Copyright (c) 2006 John Wiley & Sons, Ltd.

关键词： annihilator method approximate null-spaces Jacobi-Davidson singular value decomposition deflation stagnation

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A simple and efficient algorithm for eigenvalues computation

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6th International conference on numerical methods and applications

作者： Alt, Rene Univ Paris 06 Lab LIP6 CNRS UMR 7606 F-75230 Paris France

ISBN: (纸本)9783540709404

A simple algorithm for the computation of eigenvalues of real or complex square matrices is proposed. This algorithm is based on an additive decomposition of the matrix. A sufficient condition for convergence is proved. It is also shown that this method has many properties of the QR algorithm : it is invariant for the Hessenberg form, shifts are possible in the case of a null element on the diagonal. Some other interesting experimental properties are shown. numerical experiments are given showing that most of the time the behavior of this method is not much different from that of the QR method, but sometimes it gives better results, particularly in the case of a bad conditioned real matrix having real eigenvalues.

关键词： linear algebra eigenvalues computation CESTAC method

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Polarimetric angular smoothing algorithm for an electromagnetic vector-sensor array

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IET RADAR SONAR AND NAVIGATION 2007年第3期1卷 230-240页

作者： Xu, Y. Liu, Z. Beijing Inst Technol Dept Elect Engn Beijing 100081 Peoples R China

The polarimetric angular smoothing (PAS) technique for coherent direction-of-arrival (DOA) estimation and adaptive beamforming is explored and enriched by taking into account the cross-correlations among the smoothed subarrays and using non-uniform weights. The PAS using annihilating weights is shown to be free of signal cancellation [ which occurs in the conventional spatial smoothing (SS) technique for uncorrelated sources] while effectively suppressing coloured noise with unknown Toeplitz covariance matrix, but may be incompetent for DOA estimation. The PAS technique is still shown to be more attractive than the SS scheme in a very difficult situation that the direct signals and the reflecting signals are of very close DOAs. The penalised Toeplitz-block-Toeplitz scheme is further suggested for more thorough source decorrelation with an L-shaped electromagnetic vector-sensor array to gain improved interference suppression. The analytical expression for the mean-squared error of DOA estimates obtained from the weight-PAS pre-processed root-multiple signal classification is derived and analysed. A hybrid DOA estimator incorporating PAS and integrating some existing techniques is also described. numerical results are finally given.

关键词： Electromagnetic compatibility and interference Toeplitz matrices linear algebra (numerical analysis) Signal processing and detection correlation methods electromagnetic devices coherent direction-of-arrival estimation annihilating weight Toeplitz covariance matrix coloured noise suppression weight-PAS pre-processed root-multiple signal classification polarimetric angular smoothing algorithm adaptive beamforming mean-squared error covariance matrices Electromagnetic device applications mean square error methods Signal processing theory L-shaped electromagnetic vector-sensor array smoothing methods signal cancellation array signal processing Interpolation and function approximation (numerical analysis) DOA direction-of-arrival estimation cross-correlation signal classification interference suppression

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Multilevel preconditioning of 2D Rannacher-Turek FE problems;Additive and multiplicative methods

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6th International conference on numerical methods and applications

作者： Georgiev, Ivan Kraus, Johannes Margenov, Svetozar Bulgarian Acad Sci Inst Parallel Proc Inst Math & Informat BG-1113 Sofia Bulgaria Johann Radon Inst Computat & Appl Math A-4040 Linz Austria Bulgarian Acad Sci Inst Parallel Proc BU-1113 Sofia Bulgaria

ISBN: (纸本)9783540709404

In the present paper we concentrate on algebraic two-level and multilevel preconditioners for symmetric positive definite problems arising from discretization by Rannacher-Turek non-conforming rotated bilinear finite elements on quadrilaterals. An important point to make is that in this case the finite element spaces corresponding to two successive levels of mesh refinement are not nested (in general). To handle this, a proper two-level basis is required in order to fit the general framework for the construction of two-level preconditioners for conforming finite elements and to generalize the methods to the multilevel case. The proposed variants of hierarchical two-level basis are first introduced in a rather general setting. Then, the involved parameters are studied and optimized. As will be shown, the obtained bounds - in particular - give rise to optimal order AMLI methods of additive type. The presented numerical tests fully confirm the theoretical estimates.

关键词： linear algebra

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Unified theory of complex-valued matrix differentiation

Unified theory of complex-valued matrix differentiation

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32nd IEEE International conference on Acoustics, Speech and Signal Processing

作者： Hjorungnes, Are Gesbert, David Palomar, Daniel P. Univ Oslo UniK Univ Grad Ctr Instituttveien 25POB 70 N-2027 Kjeller Norway Eurecorm Inst Mobile Commun Dept F-06904 Sophia France Hong Kong Univ Sci & Technol Dept Elect & Comp Engn Kowloon Hong Kong Peoples R China

ISBN: (纸本)1424407281

A systematic theory is introduced for finding the derivatives of complex-valued matrix functions with respect to a complex-valued matrix variable and the complex conjugate of this variable. In the framework introduced, the differential of the complex-valued matrix function is used to identify the derivatives of this function. Matrix differentiation results are developed for use in signal processing and communications applications. Several other examples are given.

关键词： adaptive filters optimization methods gradient methods linear algebra

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Some applications of interval analysis to statistical problems

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9th International Work-conference on Artificial Neural Networks

作者： Vigneron, Vincent IBISC CNRS FRE 2873 F-91020 Evry France

ISBN: (纸本)9783540730064

This paper contribution is about guaranteed numerical methods based on interval analysis for approximating sets, and about the application of these methods to vast classes of statistical problems. 'Guaranteed' means here the inner and outer approximations of the sets of interest are obtained, which can be made as precise as desired, at the cost of increasing the computational effort. It thus becomes possible to archieve tasks still thought by many to be out of the reach of numerical methods, such as finding all solutions of sets of non-linear equations and inequalities or a global optimizer of possible multi-modal criteria.

关键词： Approximation theory

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Coordinate and subspace optimization methods for linear least squares with non-quadratic regularization

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APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS 2007年第3期23卷 346-367页

作者： Elad, Michael Matalon, Boaz Zibulevsky, Michael Technion Israel Inst Technol Dept Comp Sci IL-32000 Haifa Israel Technion Israel Inst Technol Dept Elect Engn IL-32000 Haifa Israel

This work addresses the problem of regularized linear least squares (RLS) with non-quadratic separable regularization. Despite being frequently deployed in many applications, the RLS problem is often hard to solve using standard iterative methods. In a recent work [M. Elad, Why simple shrinkage is still relevant for redundant representations? IEEE Trans. Inform. theory 52 (12) (2006) 5559-5569], a new iterative method called parallel coordinate descent (PCD) was devised. We provide herein a convergence analysis of the PCD algorithm, and also introduce a form of the regularization function, which permits analytical solution to the coordinate optimization. Several other recent works [I. Daubechies, M. Defrise, C. De-Mol, An iterative thresholding algorithm for linear inverse problems with a sparsity constraint, Comm. Pure Appl. Math. LVII (2004) 1413-1457;M.A. Figueiredo, R.D. Nowak, An EM algorithm for wavelet-based image restoration, IEEE Trans. Image Process. 12 (8) (2003) 906-916;M.A. Figueiredo, R.D. Nowak, A bound optimization approach to wavelet-based image deconvolution, in: IEEE International conference on Image Processing, 2005], which considered the deblurring problem in a Bayesian methodology, also obtained element-wise optimization algorithms. We show that the last three methods are essentially equivalent, and the unified method is termed separable surrogate functionals (SSF). We also provide a convergence analysis for SSE To further accelerate PCD and SSF, we merge them into a recently developed sequential subspace optimization technique (SESOP), with almost no additional complexity. A thorough numerical comparison of the denoising application is presented, using the basis pursuit denoising (BPDN) objective function, which leads all of the above algorithms to an iterated shrinkage format. Both with synthetic data and with real images, the advantage of the combined PCD-SESOP method is demonstrated. (c) 2007 Elsevier Inc. All rights reserved.

关键词： least squares regularization inverse problems denoising shrinkage basis pursuit sparsity coordinate-descent proximal-point

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Symbolic and algebraic methods for linear partial differential operators

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10th International Workshop on Computer algebra in Scientific Computing

作者： Winkler, Franz Shemyakova, Ekaterina RISC Linz Austria

ISBN: (纸本)9783540751861

The solution of Partial Differential Equations (PDEs) is one of the most important problems of mathematics, and has an enormous area of applications. One of the methods for extending the range of analytically solvable PDEs consists in transformations of PDEs and the corresponding transformations of their solutions. Thus, based on the fact that a second-order equation can be solved if one of its factorizations is known, the famous method of Laplace Transformations suggests a certain sequence of transformations of a given equation. Then, if at a certain step in this transformation process an equation becomes factorizable, an analytical solution of this transformed equation - and then of the initial one - can be found. The aim of this talk is a description of some old and new developments and generalizations of analytical approaches to the solution of PDEs and the corresponding algebraic theory of differential operators. Recently we have introduced the notion of obstacle for the factorization of a differential operator, i.e. conditions preventing a given operator from being factorizable. These obstacles give rise to a ring of obstacles and furthermore to a classification of operators w.r.t. to their factorization properties. From obstacles we can also get (Laplace) invariants of operators w.r.t. to certain (gauge) transformations. We have shown how such systems of invariants can be extended to full systems of invariants for certain low order operators. Another related problem is the description of the structure of families of factorizations. For operators of order 3 it has been shown that a family of factorizations depends on at most 3 or 2 parameters, each of these parameters being a function on one variable. © Springer-Verlag Berlin Heidelberg 2007.

关键词： numerical methods

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numerical Analysis and Applied Mathematics: International conference of numerical Analysis and Applied Mathematics

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2007年

作者： Theodore E Simos Georgios Y Psihoyios Ch Tsitouras

ISBN: (纸本)9780735404472

All papers have been peer-reviewed. The International conference on numerical Analysis and Applied Mathematics 2007 (ICNAAM-2007) has been scheduled to take place at Hotel Marbella in Corfu between 16th and 20th September 2007. The aim of the conference is to bring together leading scientists of the international numerical and Applied Mathematics community and to attract original research papers of very high quality. More than 350 papers have been submitted in order to be considered for presentation at ICNAAM-2007. From these submissions we have selected 189 papers after an international peer review by at least two independent reviewers. Topics to be covered include (but are not limited to): All the research areas of numerical Analysis and Computational Mathematics (numerical ODEs, numerical PDEs (inc. BVPs), Scientific Computing and Algorithms, Stochastic Differential Equations, Approximation, numerical linear algebra, numerical Integral Equations, Error Analysis and Interval Analysis, Difference Equations and Recurrence Relations, numerical problems in Dynamical Systems, applications to the Sciences (Computational Physics, Computational Statistics, Computational Chemistry, Computational Engineering etc.), Differential algebraic Equations, numerical methods in Fourier analysis etc). All the research areas of Applied and Industrial Mathematics (Mathematical Physics, Mathematical Chemistry, Mathematical Biology and Mathematical Medicine, Optimization and Operational Research, Theoretical Mechanics, Discrete Applied Mathematics, Statistics, Probability, Dynamical Systems, Algorithms, Experimental Mathematics, Theoretical Computer Science, Applied Analysis, Mathematical Modelling (including but not limited to mathematical modelling of engineering and environmental processes, manufacturing, and industrial systems, heat transfer, fluid mechanics, CFD, and transport phenomena; solid mechanics and mechanics of metals; electromagnets and MHD; reliability modelling and syste

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