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A note on simultaneous preconditioning and symmetrization of non-symmetric linear systems

numerical linear algebra WITH applications 2011年第3期18卷 343-349页

作者： Ghoussoub, Nassif Moradifam, Amir Univ British Columbia Dept Math Vancouver BC V6T 1Z2 Canada

Motivated by the theory of self-duality that provides a variational formulation and resolution for non-self-adjoint partial differential equations (Ann. Inst. Henri Poincare (C) Anal Non Lineaire 2007;24:171-205;Selfdual Partial Differential Systems and Their Variational Principles. Springer: New York, 2008), we propose new templates for solving large non-symmetric linear systems. The method consists of combining a new scheme that simultaneously preconditions and symmetrizes the problem, with various well-known iterative methods for solving linear and symmetric problems. The approach seems to be efficient when dealing with certain ill-conditioned, and highly non-symmetric systems. The numerical and theoretical results are provided to show the efficiency of our approach. Copyright (C) 2010 John Wiley & Sons, Ltd.

关键词： iterative methods sparse matrices Lanczos methods

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A Class of Fast Quaternion Valued Variable Stepsize Stochastic Gradient Learning Algorithms for Vector Sensor Processes

A Class of Fast Quaternion Valued Variable Stepsize Stochast...

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International Joint conference on Neural Networks (IJCNN)

作者： Wang, Mingxuan Took, Clive Cheong Mandic, Danilo P. Univ London Imperial Coll Sci Technol & Med Dept Elect Engn London SW7 2AZ England

ISBN: (纸本)9781424496365

We introduce a class of gradient adaptive stepsize algorithms for quaternion valued adaptive filtering based on three-and four-dimensional vector sensors. This equips the recently introduced quaternion least mean square (QLMS) algorithm with enhanced tracking ability and enables it to be more responsive to dynamically changing environments, while maintaining its desired characteristics of catering for large dynamical differences and coupling between signal components. For generality, the analysis is performed for the widely linear signal model, which by virtue of accounting for signal noncircularity, is optimal in the mean squared error (MSE) sense for both second order circular (proper) and noncircular (improper) processes. The widely linear QLMS (WL-QLMS) employing the proposed adaptive stepsize modifications is shown to provide enhanced performance for both synthetic and real world quaternion valued signals. Simulations include signals with drastically different component dynamics, such as four dimensional quaternion comprising three dimensional turbulent wind and air temperature for renewable energy applications.

关键词： Adaptation models algebra Heuristic algorithms Prediction algorithms Quaternions Signal processing Signal processing algorithms adaptive stepsize modification air temperature component dynamics fast quaternion valued variable stepsize stochastic gradient learning algorithm filtering theory four dimensional quaternion four-dimensional vector sensor gradient adaptive stepsize algorithm gradient methods mean square error methods mean squared error quaternion least mean square quaternion valued adaptive filtering real world quaternion valued signal renewable energy application signal noncircularity signal processing three dimensional turbulent wind three-dimensional vector sensor tracking ability vector sensor process vectors

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Efficient Model Order Reduction of Large-Scale Systems on Multi-core Platforms

Efficient Model Order Reduction of Large-Scale Systems on Mu...

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11th International conference on Computational Science and Its applications (ICCSA)

作者： Ezzatti, P. Quintana-Orti, E. S. Remon, A. Univ Republica Ctr Calculo Inst Comp Montevideo Uruguay Univ Jaume Dept Ingn Ciencia Comp Castellon de la Plana Spain

ISBN: (纸本)9783642219337;9783642219344

We propose an efficient implementation of the Balanced Truncation (BT) method for model order reduction when the state-space matrix is symmetric (positive definite). Most of the computational effort required by this method is due to the computation of matrix inverses. Two alternatives for the inversion of a symmetric positive definite matrix on multi-core platforms are studied and evaluated, the traditional approach based on the Cholesky factorization and the Gauss-Jordan elimination algorithm. Implementations of both methods have been developed and tested. numerical experiments show the efficiency attained by the proposed implementations on the target architecture.

关键词： Model reduction linear algebra matrix inversion SPD matrices SVD-based methods multi-core processors BLAS

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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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2011 20th European conference on Circuit theory and Design, ECCTD 2011

作者： Soudan, Michael Vogel, Christian Signal Processing and Speech Communication Laboratory Graz University of Technology A-8010 Graz Austria Telecommunications Research Center Vienna A-1220 Vienna Austria

ISBN: (纸本)9781457706189

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. © 2011 IEEE.

关键词： Time varying systems

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Normal estimation on manifolds by gradient learning

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numerical linear algebra WITH applications 2011年第2期18卷 249-259页

作者： Shi, Lei Zhou, Ding-Xuan City Univ Hong Kong Dept Math Kowloon Hong Kong Peoples R China Univ Sci & Technol China Joint Adv Res Ctr Suzhou 215123 Jiangshu Peoples R China City Univ Hong Kong Suzhou 215123 Jiangshu Peoples R China

Normal estimation is an important topic for processing point cloud data and surface reconstruction in computer graphics. In this paper we consider the problem of estimating normals for a (unknown) submanifold of a Euclidean space of codimension 1 from random points on the manifold. We propose a kernel-based learning algorithm in an unsupervised form of gradient learning. The algorithm can be implemented by solving a linear algebra problem. Error analysis is conducted under conditions on the true normals of the manifold and the sampling distribution. Copyright (C) 2010 John Wiley & Sons, Ltd.

关键词： normal estimation learning theory linear algebra reproducing kernel Hilbert space gradient learning Riemannian manifold

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numerical-analytical implementation of Galerkin technique for analysis of waveguide and slotted waveguide antenna arrays

Numerical-analytical implementation of Galerkin technique fo...

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8th International conference on Antenna theory and Techniques, ICATT'11

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

ISBN: (纸本)9781467300018

A novel fast and accurate full-wave approach to the analysis of a wide class of slotted waveguide arrays and finite multilayer 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 multilayer dielectric cover is presented, which includes the effect of dielectric cover on impedance matching, array efficiency and directivity. © 2011 IEEE.

关键词： Galerkin methods

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Momentum algorithms in neural networks and the applications in numerical algebra

Momentum algorithms in neural networks and the applications ...

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International conference on Artificial Intelligence, Management Science and Electronic Commerce (AIMSEC)

作者： Naimin Zhang School of Mathematics and Information Science Wenzhou University Wenzhou China

Momentum algorithms in neural networks and the applications for solving linear systems are discussed. The sufficient and necessary conditions for the convergence of the stationary iteration with momentum acceleration are obtained. Furthermore, the optimal momentum factor which minimizes the spectral radius of the associated momentum acceleration iteration matrix is also obtained. Some numerical results have demonstrated the effectiveness of the stationary iterations with momentum acceleration.

关键词： Convergence linear systems Jacobian matrices Eigenvalues and eigenfunctions Acceleration Gradient methods Neural networks

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Ill-conditioning of the truncated singular value decomposition, Tikhonov regularization and their applications to numerical partial differential equations

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numerical linear algebra WITH applications 2011年第2期18卷 205-221页

作者： Li, Zi-Cai Huang, Hung-Tsai Wei, Yimin Fudan Univ Sch Math Sci Shanghai 200433 Peoples R China Natl Sun Yat Sen Univ Dept Appl Math Kaohsiung 80424 Taiwan Natl Sun Yat Sen Univ Dept Comp Sci & Engn Kaohsiung 80424 Taiwan I Shou Univ Dept Appl Math Kaohsiung 84001 Taiwan Shanghai Key Lab Contemporary Appl Math Shanghai 200433 Peoples R China

This paper explores some intrinsic characteristics of accuracy and stability for the truncated singular value decomposition (TSVD) and the Tikhonov regularization (TR), which can be applied to numerical solutions of partial differential equations (numerical PDE). The ill-conditioning is a severe issue for numerical methods, in particular when the minimal singular value sigma(min) of the stiffness matrix is close to zero, and when the singular vector mu(min) of sigma(min) is highly oscillating. TSVD and TR can be used as numerical techniques for seeking stable solutions of linear algebraic equations. In this paper, new bounds are derived for the condition number and the effective condition number which can be used to improve ill-conditioning by TSVD and TR. A brief error analysis of TSVD and TR is also made, since both errors and condition number are essential for the numerical solution of PDE. numerical experiments are reported for the discrete Laplace operator by the method of fundamental solutions. Copyright (C) 2011 John Wiley & Sons, Ltd.

关键词： ill-conditioning fundamental solutions truncated singular value decomposition Tikhonov regularization effective condition number collocation Trefftz method

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Accelerated direct solution of the MoM linear system using block compression and nested factorization

Accelerated direct solution of the MoM linear system using b...

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International conference on Electromagnetics in Advanced applications (ICEAA)

作者： A. Heldring J.M. Rius Department of Telecommunications and Signal Processing Polytechnic University of Catalonia Barcelona Spain

A comparison is presented between different algorithms for direct (non-iterative) accelerated solution of the Method of Moments. The alternatives are common block LU factorization and Compressed Block Decomposition (CBD), and their respective nested, or Multi Scale (MS) implementations. The comparison includes theoretical considerations and numerical examples.

关键词： Matrix decomposition Moment methods NASA Impedance Algorithm design and analysis Complexity theory linear systems

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The analysis of the parameter involving in the shift technique for nonsymmetric algebraic Riccati equations

The analysis of the parameter involving in the shift techniq...

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International conference on Multimedia Technology

作者： Xiangyin Kong Department of mathematics University of Zhejiang Hangzhou China

ISBN: (纸本)9781612847719

The minimal positive solution of nonsymmetric algebraic Riccati equations arising from transport theory, can be obtained by computing the one of two vector equations. Some existing methods such as simple iteration method, converge slowly in the singular case, but this drawback can be improved with the shift technique. When using the shift technique, a parameter will be used. In this paper, the parameter's effects on the convergence rate of four existing methods for solving the vector equations and its optimal value in a given interval is given. numerical results are presented to demonstrate theoretical analysis.

关键词： Riccati equations Silicon Iterative methods Convergence Eigenvalues and eigenfunctions linear algebra

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