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Numerical Solution of Bratu's Problem Using Multilayer Perceptron Neural Network Method

NATIONAL ACADEMY SCIENCE LETTERS-INDIA 2015年第5期38卷 425-428页

作者： Kumar, Manoj Yadav, Neha Motilal Nehru Natl Inst Technol Dept Math Allahabad 211004 Uttar Pradesh India ITM Univ Dept Appl Sci Gurgaon 122017 Haryana India

In this article, an artificial neural network (ANN) method is presented to obtain the closed analytic form of the one dimensional Bratu type equations, which are widely applicable in fuel ignition of the combustion theory and heat transfer. Our goal is to provide optimal solution of Bratu type equations with reduced calculus effort using ANN method in comparison to the other existing methods. Various test cases have been simulated using proposed neural network model and the accuracy has been substantiated by considering a large number of simulation data for each model with enough independent runs. Numerical results show that this method has potentiality to become an efficient approach for solving Bratu's problems with less computing time and memory space.

关键词： Artificial neural network Back propagation algorithm Bratu's equations Levenberg-Marquardt algorithm conjugate gradient algorithm

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Time-harmonic solution for acousto-elastic interaction with controllability and spectral elements

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2010年第6期234卷 1904-1911页

作者： Monkola, Sanna Univ Jyvaskyla Dept Math Informat Technol FI-40014 Jyvaskyla Finland

The classical way of solving the time-harmonic linear acousto-elastic wave problem is to discretize the equations with finite elements or finite differences. This approach leads to large-scale indefinite complex-valued linear systems. For these kinds of systems, it is difficult to construct efficient iterative solution methods. That is why we use an alternative approach and solve the time-harmonic problem by controlling the solution of the corresponding time dependent wave equation. In this paper, we use an unsymmetric formulation, where fluid-structure interaction is modeled as a coupling between pressure and displacement. The coupled problem is discretized in space domain with spectral elements and in time domain with central finite differences. After discretization, exact controllability problem is reformulated as a least-squares problem, which is solved by the conjugate gradient method. (C) 2009 Elsevier B.V. All rights reserved.

关键词： Fluid-structure interaction Acoustic waves Elastic waves Coupled problem Time-harmonic solution Spectral element method Controllability conjugate gradient algorithm

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LANGEVIN SIMULATIONS OF LATTICE FIELD-THEORIES USING FOURIER ACCELERATION

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JOURNAL OF STATISTICAL PHYSICS 1986年第5-6期43卷 1073-1075页

作者： DAVIES, C BATROUNI, G KATZ, G KRONFELD, A LEPAGE, P ROSSI, P SVETITSKY, B WILSON, K MIT CAMBRIDGEMA 02139 DESY HAMBURGFED REP GER

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RESPONSE IMPROVEMENTS IN INDUSTRIAL DC DRIVES DERIVED FROM OPTIMAL ANALYSIS

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IEE PROCEEDINGS-B ELECTRIC POWER APPLICATIONS 1985年第3期132卷 171-173页

作者： JONES, DI UNIV COLL N WALES SCH ELECTR ENGN SCIBANGOR LL57 1UTGWYNEDDWALES

Reference is made to a recent paper by B. J. Cardwell and C. J. Goodman (published in IEE Proc. B, Electr. Power Appl. , 1984, 131, (3), pp. 91-98) who calculate the optimal controls for a dc machine executing transient changes in speed. Their computational method is capable of dealing with armature current saturation but, unfortunately, encounters convergence difficulties in the presence of control limits. In this correspondence, the conjugate gradient algorithm is shown to overcome this difficulty. A reply by the original authors is included.

关键词： optimal control armature current saturation electric drives optimal analysis computational method optimal controls Optimal control Drives industrial DC drives DC motors conjugate gradient algorithm transient changes in speed d.c. machines convergence difficulties Control of electric power systems

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DATA-PARALLEL QUADRATIC-PROGRAMMING ON BOX-CONSTRAINED PROBLEMS

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SIAM JOURNAL ON OPTIMIZATION 1995年第3期5卷 570-589页

作者： MCKENNA, MP MESIROV, JP ZENIOS, SA UNIV PENN WHARTON SCH DEPT OPERAT & INFORMAT MANAGEMENT PHILADELPHIA PA 19104 USA UNIV CYPRUS NICOSIA CYPRUS

We develop designs for the data parallel solution of quadratic programming problems subject to box constraints. In particular, we consider the class of algorithms that iterate between projection steps that identify candidate active sets and conjugate gradient steps that explore the working space. Using the algorithm of More and Toraldo [Report MCS-p77-05 89, Argonne National Laboratory, Illinois, 1989] as a specific instance of this class of algorithms we show how its components can be implemented efficiently on a data-parallel SIMD computer architecture. Alternative designs are developed for both arbitrary, unstructured Hessian matrices and for structured problems. Implementations are carried out on a Connection Machine CM-2. They are shown to be very efficient, achieving a peak computing rate over 2 Chops. Problems with several hundred thousand variables are solved within one minute of solution time on the 8K CM-2. Extremely large test problems, with up to 2.89 million variables, are also solved efficiently. The data parallel implementation outperforms a benchmark implementation of interior point algorithms on an IBM 3090-6009 vector supercomputer and a successive overrelaxation algorithm on an Intel iPSC/860 hypercube.

关键词： LARGE-SCALE OPTIMIZATION conjugate gradient algorithm DATA STRUCTURES

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ON ADAPTIVE WEIGHTED POLYNOMIAL PRECONDITIONING FOR HERMITIAN POSITIVE-DEFINITE MATRICES

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SIAM JOURNAL ON SCIENTIFIC COMPUTING 1994年第2期15卷 408-426页

作者： FISCHER, B FREUND, RW AT&T BELL LABS MURRAY HILL NJ 07974 USA

The conjugate gradient algorithm for solving Hermitian positive definite linear systems is usually combined with preconditioning in order to speed up convergence. In recent years, there has been a revival of polynomial preconditioning, motivated by the attractive features of the method on modem architectures. Standard techniques for choosing the preconditioning polynomial are based only on bounds for the extreme eigenvalues. Here a different approach is proposed that aims at adapting the preconditioner to the eigenvalue distribution of the coefficient matrix. The technique is based on the observation that good estimates for the eigenvalue distribution can be derived after only a few steps of the Lanczos process. This information is then used to construct a weight function for a suitable Chebyshev approximation problem. The solution of this problem yields the polynomial preconditioner. In particular, polynomial preconditioners associated with Bernstein-Szego weights are studied. Results of numerical experiments are reported.

关键词： LINEAR SYSTEMS HERMITIAN POSITIVE DEFINITE MATRICES conjugate gradient algorithm POLYNOMIAL PRECONDITIONING CHEBYSHEV APPROXIMATION PROBLEM BERNSTEIN-SZEGO WEIGHTS

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Improved BP neural network based active disturbance rejection control for magnetic sensitivity calibration system 12

Improved BP neural network based active disturbance rejectio...

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IEEE 12th Data Driven Control and Learning Systems Conference (DDCLS)

作者： Wang, Minlin Dong, Xueming Ren, Xuemei Changcheng Inst Metrol & Measurement Dept Inertia Beijing 100095 Peoples R China Beijing Inst Technol Sch Automat Beijing 100081 Peoples R China

ISBN: (纸本)9798350321050

In the magnetic sensitivity calibration system, the calibration accuracy of inertial sensor is directly related to the control accuracy of the magnetic induction intensity. Since the helmholtz coils in the calibration system have large parameter uncertainties and the magnetic field sensor has some time-delay, the traditional PID controller cannot satisfy the accuracy requirement of the magnetic induction intensity. Therefore, an improved neural network based active disturbance rejection controller (ADRC) is proposed, which utilizes the conjugate gradient algorithm and Fletcher-Reeves linear search method to adjust the parameters of ADRC for achieving the optimal control efforts. Moreover, the extended state observer of ADRC can compensate for the parameter uncertainties and time-delay exactly such that the control accuracy of the magnetic induction intensity can be largely improved. The simulations are conducted to show the effectiveness and superiority of the proposed control algorithm.

关键词： magnetic sensitivity calibration system parameter uncertainties and time-delay ADRC neural network conjugate gradient algorithm Fletcher-Reeves linear search method

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WLAN location determination model based on the artificial neural networks

WLAN location determination model based on the artificial ne...

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47th International Symposium ELMAR-2005 on Multimedia Systems and Applications

作者： Vilovic, I Zovko-Cihlar, B Univ Dubrovnik Dept Elect Engn & Comp Dubrovnik Croatia

ISBN: (纸本)9537044041

Along with increasing popularity of wireless LAN, problem of location determination for mobile users becomes more important. The strengths of RF signals arriving from several access points can be used for location determination of the mobile terminal. In indoor environments the received signal level is very complex function of the distance. The solution can be found in the area of artificial neural networks. The neural networks can be learned to classify data. Labeled data examples of signal strengths at known locations must be collected by the measurement. This data will serve for the training of the network with appropriate training algorithm. The trained network is capable to determine location on the base of new signal strengths as a process of generalization. The advantage of the method is that it doesn't need any extra hardware, while with flexible neural network model achieves lower distance errors in determining position comparable with other methods. For successful position determination only what is needed are a map of indoor space and several identified locations to train the network.

关键词： WLAN artificial neural network location determination synaptic weights activation function back-propagation algorithm conjugate gradient algorithm

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Accelerating Numerical Linear Algebra Kernels on a Scalable Run Time Reconfigurable Platform

Accelerating Numerical Linear Algebra Kernels on a Scalable ...

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IEEE Annual Symposium on VLSI (ISVLSI)

作者： Biswas, Prasenjit Udupa, Pramod P. Mondal, Rajdeep Varadarajan, Keshavan Alle, Mythri Nandy, S. K. Narayan, Ranjani CADL IISc Bangalore Karnataka India Morphing Machines Bangalore Karnataka India

ISBN: (纸本)9780769540764

Numerical Linear Algebra (NLA) kernels are at the heart of all computational problems. These kernels require hardware acceleration for increased throughput. NLA Solvers for dense and sparse matrices differ in the way the matrices are stored and operated upon although they exhibit similar computational properties. While ASIC solutions for NLA Solvers can deliver high performance, they are not scalable, and hence are not commercially viable. In this paper, we show how NLA kernels can be accelerated on REDEFINE, a scalable runtime reconfigurable hardware platform. Compared to a software implementation, Direct Solver (Modified Faddeev's algorithm) on REDEFINE shows a 29x improvement on an average and Iterative Solver (conjugate gradient algorithm) shows a 15-20% improvement. We further show that solution on REDEFINE is scalable over larger problem sizes without any notable degradation in performance.

关键词： ASIC solutions conjugate gradient Direct Solver Faddeev's algorithm Iterative Solver NLA kernels NLA solvers Numerical Linear Algebra REDEFINE Runtime reconfiguration Systolic array computational property conjugate gradient algorithm conjugate gradient methods dense matrices direct solver hardware acceleration linear algebra modified Faddeev's algorithm numerical linear algebra kernels reconfigurable architectures scalable run time reconfigurable platform software implementation sparse matrices sparse matrices

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Complex Blind Source Separation via Simultaneous Strong Uncorrelating Transform 1

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9th International Conference on Latent Variable Analysis and Signal Separation

作者： Shen, Hao Kleinsteuber, Martin Tech Univ Munich Inst Data Proc D-8000 Munich Germany

ISBN: (数字)9783642159954

ISBN: (纸本)9783642159947

In this paper, we address the problem of complex blind source separation (BSS), in particular, separation of nonstationary complex signals. It is known that, under certain conditions, complex BSS can be solved effectively by the so-called Strong Uncorrelating Transform (SUT), which simultaneously diagonalizes one Hermitian positive definite and one complex symmetric matrix. Our current work generalizes SUT to simultaneously diagonalize more than two matrices. A conjugate gradient (CG) algorithm for computing simultaneous SUT is developed on an appropriate manifold setting of the problem, namely complex oblique projective manifold. Performance of our method, in terms of separation quality, is investigated by several numerical experiments.

关键词： Complex blind source separation nonstationary signal simultaneous strong uncorrelating transform complex oblique projective manifold conjugate gradient algorithm

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