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23rd European Signal Processing Conference (EUSIPCO)

作者： Cherrak, O. Ghennioui, H. Abarkan, E. -H. Thirion-Moreau, N. Moreau, E. Univ Sidi Mohamed Ben Abdellah FSTF LSSC Route ImmouzzerBP 2202 Fes Morocco Univ Aix Marseille CNRS ENSAM LSISUMR 7296 F-13397 Marseille France Univ Toulon & Var CNRS LSIS UMR 7296 F-83957 La Garde France

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 conjugate gradient 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.

关键词： Joint zero-block diagonalization matrix decompositions conjugate gradient algorithm linear convolutive mixtures

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A conjugate gradient algorithm FOR BLIND SENSOR CALIBRATION IN SPARSE RECOVERY

A CONJUGATE GRADIENT ALGORITHM FOR BLIND SENSOR CALIBRATION ...

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23rd IEEE International Workshop on Machine Learning for Signal Processing (MLSP)

作者： Shen, Hao Kleinsteuber, Martin Bilen, Cagdas Gribonval, Remi Tech Univ Munich D-80333 Munich Germany INRIA Ctr Inria Rennes F-35042 Rennes France

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 conjugate gradient method. Several numerical experiments are provided to oppose our approach to the solutions given by convex optimization and to demonstrate its performance.

关键词： Blind sensor calibration compressive sensing conjugate gradient algorithm

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Modified Incomplete Cholesky Preconditioned conjugate gradient algorithm on GPU for the 3D Parabolic Equation

Modified Incomplete Cholesky Preconditioned Conjugate Gradie...

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10th IFIP International Conference on Network and Parallel Computing (NPC)

作者： Gao, Jiaquan Li, Bo He, Guixia Zhejiang Univ Technol Coll Comp Sci & Technol Hangzhou 310023 Zhejiang Peoples R China Zhejiang Univ Technol Zhejiang Coll Hangzhou 310024 Zhejiang Peoples R China

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.

关键词： conjugate gradient algorithm modified incomplete Cholesky preconditioner parabolic equation GPU

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Application of neural networks trained with an improved conjugate gradient algorithm to the turbine fast valving control

Application of neural networks trained with an improved conj...

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International Conference on Power System Technology (POWERCON 2000)

作者： Zhang, LZ Kang, JP Lin, XS Xu, YG N China Elect Power Univ Beijing 102206 Peoples R China

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.

关键词： conjugate gradient algorithm neural network fast valving transient stability

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A Bi-matrix-based conjugate gradient algorithm for the WLS Design of Centro-symmetric 2-D FIR Filters 23

A Bi-matrix-based Conjugate Gradient Algorithm for the WLS D...

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23rd IEEE International Conference on Digital Signal Processing (DSP)

作者： Zhao, Ruijie Lai, Xiaoping Lin, Zhiping Gao, Zhifeng Shandong Univ Sch Mech Elect & Informat Engn Weihai Peoples R China Hangzhou Dianzi Univ Inst Informat & Control Hangzhou Zhejiang Peoples R China Nanyang Technol Univ Sch Elect & Elect Engn Singapore Singapore

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.

关键词： Centro-symmetric 2-D FIR Filter conjugate gradient algorithm Weighted Least Squares Design

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A conjugate gradient algorithm with Yuan-Wei-Lu Line Search 3rd

A Conjugate Gradient Algorithm with Yuan-Wei-Lu Line Search

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3rd International Conference on Cloud Computing and Security (ICCCS)

作者： Yuan, Gonglin Hu, Wujie Sheng, Zhou Guangxi Univ Coll Math & Informat Sci Nanning 530004 Guangxi Peoples R China Nanjing Univ Informat Sci & Technol Sch Comp & Software Nanjing 210044 Jiangsu Peoples R China

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... 详细信息

ISBN: (纸本)9783319685427;9783319685410

关键词： conjugate gradient algorithm Optimization Line search Convergence

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Improved preconditioned conjugate gradient algorithm and application in 3D inversion of gravity-gradiometry data

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Applied Geophysics 2017年第2期14卷 301-313,324页

作者： Wang Tai-Han Huang Da-Nian Ma Guo-Qing Meng Zhao-Hai Li Ye College of Geo-Exploration Scienceand Technology Jilin University Claangchun 130021 China Tianjin Navigation Instrument Research Institute Tianjin 300131 China Jilin Provincial Electric Power Survey and Design Institute Changchun 130021 China.

With the continuous development of full tensor gradiometer （FTG） measurement techniques, three-dimensional （3D） inversion of FTG data is becoming increasingly used in oil and gas exploration. In the fast processing and interpretation of large-scale high-precision data, the use of the graphics processing unit process unit （GPU） and preconditioning methods are very important in the data inversion. In this paper, an improved preconditioned conjugate gradient algorithm is proposed by combining the symmetric successive over-relaxation （SSOR） technique and the incomplete Choleksy decomposition conjugate gradient algorithm （ICCG）. Since preparing the preconditioner requires extra time, a parallel implement based on GPU is proposed. The improved method is then applied in the inversion of noise- contaminated synthetic data to prove its adaptability in the inversion of 3D FTG data. Results show that the parallel SSOR-ICCG algorithm based on NVIDIA Tesla C2050 GPU achieves a speedup of approximately 25 times that of a serial program using a 2.0 GHz Central Processing Unit （CPU）. Real airbome gravity-gradiometry data from Vinton salt dome （south- west Louisiana, USA） are also considered. Good results are obtained, which verifies the efficiency and feasibility of the proposed parallel method in fast inversion of 3D FTG data.

关键词： Full Tensor Gravity Gradiometry (FTG) ICCG method conjugate gradient algorithm gravity-gradiometry data inversion CPU and GPU

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Error Norm Estimation in the conjugate gradient algorithm

Error Norm Estimation in the Conjugate Gradient Algorithm

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丛书名： SIAM Spotlights

2024年

作者： Gérard Meurant Petr Tichý

ISBN: (数字)9781611977868

ISBN: (纸本)9781611977851

The conjugate gradient (CG) algorithm is almost always the iterative method of choice for solving linear systems with symmetric positive definite matrices. This book describes and analyzes techniques based on Gauss quadrature rules to cheaply compute bounds on norms of the error. The techniques can be used to derive reliable stopping criteria. Computation of estimates of the smallest and largest eigenvalues during CG iterations is also shown. The algorithms are illustrated by many numerical experiments, and they can be easily incorporated into existing CG codes.

关键词： conjugate gradient algorithm linear system of equations error norms bounds of error norms eigenvalues Gauss quadrature rule Gauss-Radau quadrature rule tridiagonal matrices adaptive algorithms

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Low-complexity conjugate gradient algorithm for array code acquisition

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IEICE TRANSACTIONS ON COMMUNICATIONS 2007年第5期E90B卷 1193-1200页

作者： Yang, Hua-Lung Wu, Wen-Rong Natl Chiao Tung Univ Dept Commun Engn Hsinchu Taiwan

An adaptive array code acquisition for direct-sequence/ code-division multiple access (DS/CDMA) systems was recently proposed to enhance the performance of the conventional correlator-based method. The scheme consists of an adaptive spatial and an adaptive temporal filter, and can simultaneously perform beamforming and code-delay estimation. Unfortunately, the scheme uses a least-mean-square (LMS) adaptive algorithm, and its convergence is slow. Although the recursive-least-squares (RLS) algorithm can be applied, the computational complexity will greatly increase. In this paper, we solve the dilemma with a low-complexity conjugate gradient (LCG) algorithm, which can be considered as a special case of a modified conjugate gradient (MCG) algorithm. Unlike the original conjugate gradient (CG) algorithm developed for adaptive applications, the proposed method, exploiting the special structure inherent in the input correlation matrix, requires a low computational-complexity. It can be shown that the computational complexity of the proposed method is on the same order of the LMS algorithm. However, the convergence rate is improved significantly. Simulation results show that the performance of adaptive array code acquisition with the proposed CG algorithm is comparable to that with the original CG algorithm.

关键词： code acquisition synchronization DS/CDMA antenna arrays adaptive filtering conjugate gradient algorithm

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Scaled memoryless BFGS preconditioned conjugate gradient algorithm for unconstrained optimization (vol 22, pg 561, 2007)

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OPTIMIZATION METHODS & SOFTWARE 2013年第1期28卷 217-219页

作者： Babaie-Kafaki, Saman Semnan Univ Fac Math Stat & Comp Sci Dept Math Semnan Iran Inst Res Fundamental Sci IPM Sch Math Tehran Iran

In Andrei [Scaled memoryless BFGS preconditioned conjugate gradient (CG) algorithm for unconstrained optimization, Optim. Meth. Softw. 22(4) (2007), pp. 561-571], an efficient CG algorithm has been proposed for solving unconstrained optimization problems. However, due to a wrong inequality used in Andrei to show the sufficient descent property for the search directions, the proof of Theorem 2, the global convergence theorem, is incorrect. In what follows, the necessary corrections will be mentioned. Throughout, we use the same notations as in Andrei.

关键词： conjugate gradient algorithm sufficient descent condition line search global convergence

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