This article addresses two issues. Firstly, the convergence property of conjugategradient (CG) algorithm is investigated by a Chebyshev polynomial approximation. The analysis result shows that its convergence behavio...
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This article addresses two issues. Firstly, the convergence property of conjugategradient (CG) algorithm is investigated by a Chebyshev polynomial approximation. The analysis result shows that its convergence behaviour is affected by an acceleration term over the steepest descent (SD) algorithm. Secondly, a new CG algorithm is proposed in order to boost the tracking capability for time-varying parameters. The proposed algorithim based on re-initialising forgetting factor shows a fast tracking ability and a noise-immunity property when it encounters an unexpected parameter change. A fast tracking capability is verified through a computer simulation in a system identification problem.
Adaptive filtering using a version of the conjugategradient (CG) method which does not involve matrix inversions and is hence computationally attractive has been presented in [1]. The method,,which uses a time averag...
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Adaptive filtering using a version of the conjugategradient (CG) method which does not involve matrix inversions and is hence computationally attractive has been presented in [1]. The method,,which uses a time average over a suitably chosen window in order to generate the required gradients, has been used in [2] for the design of an adaptive beamformer. The algorithm essentially uses time diversity to obtain improved performance. We consider a modification which essentially combines spatial and time diversity to obtain an algorithm for adaptive beamforming which has potential al,plication in cellular communication systems. Simulation results are presented to demonstrate the performance of the algorithm.
We propose a new way to detect and correct silent errors in the conjugate gradient algorithm. The detection criterion is simple, cheap to implement, and can be used at each iteration. This simplifies the correction pr...
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We propose a new way to detect and correct silent errors in the conjugate gradient algorithm. The detection criterion is simple, cheap to implement, and can be used at each iteration. This simplifies the correction process. Numerical experiments show that the new criterion is robust and reliable.
We present a conjugate gradient algorithm for solving the Galerkin-characteristic approximation of interfacial flows. The governing equations are the incompressible Navier-Stokes for two fluids separated with an inter...
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We present a conjugate gradient algorithm for solving the Galerkin-characteristic approximation of interfacial flows. The governing equations are the incompressible Navier-Stokes for two fluids separated with an interface in the computational domain. We consider a level set method to track the interface in these equations. The method combines advantages of the semi-Lagrangian method to accurately solve the convection-dominated flow problems with a finite element method for space discretization of the governing equations. It can be interpreted as a fractional-step technique where the transport part and the Stokes part are treated separately. A limiting procedure is implemented for the reconstruction of numerical solutions at the departure points. The implementation of the proposed Galerkin-characteristic method differs from its Eulerian counterpart in the fact that it is applied during each time step, along the characteristic curves rather than in the time direction. Therefore, due to the Lagrangian treatment of convection, the standard Courant-Friedrichs-Levy condition is relaxed and the time truncation errors are reduced in the Stokes part. To solve the generalized Stokes problem we implement a conjugate gradient algorithm. This method avoids projection techniques and does not require any special correction for the pressure. The focus is on constructing efficient algorithms with a large stability region to solve interfacial flow problems. We verify the method for a passive transport of a slotted cylinder and for the benchmark problem of rising bubbles. We also present numerical results for a problem of barotropic flow in the Strait of Gibraltar. The conjugate gradient algorithm has been found to be feasible and satisfactory. (c) 2010 IMACS. Published by Elsevier B.V. All rights reserved.
This communication addresses a new problem which is the Non-Unitary Joint Zero-Block Diagonalization of a given set of complex matrices. This problem can occur in fields of applications such as blind separation of con...
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ISBN:
(纸本)9780992862633
This communication addresses a new problem which is the Non-Unitary Joint Zero-Block Diagonalization of a given set of complex matrices. This problem can occur in fields of applications such as blind separation of convolutive mixtures of sources and generalizes the non unitary Joint Zero-Diagonalization problem. We present a new method based on the conjugate gradient algorithm. Our algorithm uses a numerical diagram of optimization which requires the calculation of the complex gradient matrix. The main advantages of the proposed method stem from the conjugategradient properties: it is fast, stable and robust. Computer simulations are provided in order to illustrate the good behavior of the proposed method in different contexts. Two cases are studied: in the first scenario, a set of exactly zero-block-diagonal matrices are considered, then these matrices are progressively perturbed by an additive gaussian noise.
This work studies the problem of blind sensor calibration (BSC) in linear inverse problems, such as compressive sensing. It aims to estimate the unknown complex gains at each sensor, given a set of measurements of som...
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ISBN:
(纸本)9781479911806
This work studies the problem of blind sensor calibration (BSC) in linear inverse problems, such as compressive sensing. It aims to estimate the unknown complex gains at each sensor, given a set of measurements of some unknown training signals. We assume that the unknown training signals are all sparse. Instead of solving the problem by using convex optimization, we propose a cost function on a suitable manifold, namely, the set of complex diagonal matrices with determinant one. Such a construction can enhance numerical stabilities of the proposed algorithm. By exploring a global parameterization of the manifold, we tackle the BSC problem with a conjugategradient method. Several numerical experiments are provided to oppose our approach to the solutions given by convex optimization and to demonstrate its performance.
In this study, for solving the three-dimensional partial differential equation u(t) = u(xx) + u(yy) + u(zz), an efficient parallel method based on the modified incomplete Cholesky preconditioned conjugategradient alg...
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ISBN:
(纸本)9783642408199;9783642408205
In this study, for solving the three-dimensional partial differential equation u(t) = u(xx) + u(yy) + u(zz), an efficient parallel method based on the modified incomplete Cholesky preconditioned conjugate gradient algorithm (MICPCGA) on the GPU is presented. In our proposed method, for this case, we overcome the drawbacks that the MIC pre-conditioner is generally difficult to be parallelized on the GPU due to the forward/backward substitutions, and thus present an efficient parallel implementation method on the GPU. Moreover, a vector kernel for the sparse matrix-vector multiplication, and optimization of vector operations by grouping several vector operations into a single kernel are adopted. Numerical results show that our proposed forward/backward substitutions and MICPCGA on the GPU both can achieve a significant speedup, and compared to an approximate inverse SSOR pre-conditioned conjugate gradient algorithm (SSORPCGA), our proposed MICPCGA obtains a bigger speedup, and outperforms it in solving the three-dimensional partial differential equation.
The paper primarily presents an improved conjugate gradient algorithm for the neural networks training. The improved conjugate gradient algorithm introduces an approximate method for step size calculation, which does ...
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ISBN:
(纸本)0780363388
The paper primarily presents an improved conjugate gradient algorithm for the neural networks training. The improved conjugate gradient algorithm introduces an approximate method for step size calculation, which does not have the troubles in the conjugate gradient algorithm(CG) caused by the line search technique and avoids explicitly calculating the Hassian-matrix(H-matrix). It takes much less time than the error back propagation algorithm(BP) and CG for the training. The neural networks trained with the improved CG are successfully used to the fast valving control for aiding the transient stability of power systems.
The weighted least squares (WLS) design problem of centro-symmetric two-dimensional (2-D) FIR filters is investigated in this paper. Firstly, the optimality condition of the design problem is expressed as a linear ope...
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ISBN:
(纸本)9781538668122;9781538668115
The weighted least squares (WLS) design problem of centro-symmetric two-dimensional (2-D) FIR filters is investigated in this paper. Firstly, the optimality condition of the design problem is expressed as a linear operator equation in two matrix variables containing the filter design coefficients. Then by properly defining an inner product on the solution space, a bi-matrix-based conjugate gradient algorithm is obtained to solve the linear operator equation. The proposed design algorithm is shown to converge in the finite steps. An illustrative design example is given to show that the proposed algorithm consumes much less design time and has the higher design accuracy than that by some existing methods.
This paper presents a three term conjugate gradient algorithm and it has the following properties: (i) the sufficient descent property is satisfied;(ii) the algorithm has the global convergence for non-convex function...
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ISBN:
(纸本)9783319685427;9783319685410
This paper presents a three term conjugate gradient algorithm and it has the following properties: (i) the sufficient descent property is satisfied;(ii) the algorithm has the global convergence for non-convex functions;(iii) the numerical results are more effective than that of the normal algorithm.
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